There are battles throughout history that are decisive for purely military reasons, and then there are battles that are decisive for reasons that go far beyond that. Take two famous examples from the Second Punic War. Hannibal’s victory at the Battle of Cannae (216 BCE) was pretty damn decisive from a military perspective. It’s hard to get much more decisive than killing anywhere from half to 7/8 of an 80,000+ man Roman army while losing maybe a tenth of yours. You’ve clearly made a statement with a win like that. But the war went on and Rome was only temporarily weakened. The Battle of Zama (202 BCE), on the other hand, not only ended the war, but it basically ended Carthage. Yes, there was a Third Punic War, but Carthage had no ability to put up a real fight. Zama was decisive far beyond the battlefield.
The two great Arab military victories of 636, the Battle of Yarmouk against the Byzantines and the Battle of al-Qadisiyah against the Sasanian Persians, were decisive in that second, much larger, sense. Taken individually, they changed the course of both of the defeated empires: the Byzantines would never again hold significant territory south of Anatolia, and the Sasanians would never again hold, well, pretty much anything. Taken together, they changed the course of world history, ensuring that the caliphate, and therefore Islam, would spread throughout all of the vast territories that had once belonged to those two superpowers.
Truth be told, the Sasanians were already in bad shape before Qadisiyah — that might help explain why Yarmouk only shrunk the Byzantine Empire, while Qadisiyah ended the Persian Empire — owing to their defeat by the Byzantines in the war fought between the two powers between 602 and 628 and to . That war ended after the Sasanian ruler Khosrow II was overthrown by his son, Kavadh II. Kavadh died after only a few months, the victim of some kind of plague outbreak, and the resulting succession crisis touched off a civil war that–along with the plague itself, which seems to have killed a massive number of people–further weakened the already battered empire. That civil war finally ended when the 8 year old grandson of Khosrow II, Yazdegerd III (d. 651), was crowned in 632, but he was too young to rule in his own right and so the two nobles who saw to his enthronement, Rostam Farrokhzad and Piruz Khosrow, held the real power in the empire.
Meanwhile, the end of the Ridda Wars in 633 meant that caliphate had already grown to encompass all of the Arabian peninsula, so in April, with nowhere to go but north, then-Caliph Abu Bakr sent an army under his most capable general, Khalid b. al-Walid (d. 642), to conquer Iraq. Khalid had dramatic success, defeating the Persians in a series of battles that, by the end of the year, left him and his forces in control of virtually every part of Iraq outside of the Persian capital, Ctesiphon, which was located just southeast of where Baghdad is situated today. After the Battle of Firaz, in December, Abu Bakr ordered Khalid to go to Syria to assume command of the much less successful invasion of that Byzantine province, so the Persians were off the hook for a short time. In fact, as 634 wore on, the Persians began to take back some of their lost territory and defeated the Arabs in a handful of battles–though only one, the Battle of the Bridge in November, near Kufa, could be called a major victory.
In 635, Yazdegerd and the Byzantine Emperor Heraclius hatched a scheme to put down this upstart Arab incursion once and for all: a union of the two great empires sealed with a marriage between Yazdegerd and Heraclius’s daughter (which would, conveniently for the Byzantines, leave Heraclius in the dominant position as Yazdegerd’s father in-law). Both emperors planned to amass large armies to attack the Arabs simultaneously in both Syria and Iraq. The Arabs, who didn’t have enough men to sustain two large-scale offensives and were moving troops between Iraq and Syria as threats dictated, surely wouldn’t be able to handle major counter-offensives on both fronts at the same time, right?
Well, they didn’t have to find out, because Heraclius launched his offensive in May 636, and Yazdegerd…wasn’t ready. Umar b. al-Khattab, who was now caliph, helped gum up the works by sticking to Muhammad’s war-making precepts. He sent reinforcements to bolster his army in Syria while also sending a man named Saʿd ibn Abi Waqqas with a few thousand troops to Iraq, where he camped near the town of Qadisiyah, near Kufa, in July, and…that’s about it. Saʿd’s job was to engage Yazdegerd in diplomacy, to offer the Persians the chance to avoid battle either by converting to the new (and still nebulous) Islamic faith, or agreeing to pay the poll tax required of non-Muslims. This was a requirement on the Arab armies that had been imposed by Muhammad, who always offered his foes the chance to surrender before battle. But a nice side benefit of this policy for Umar, with his armies stretched thin between Syria and Iraq, was that it may have bought his army time to focus on Syria without having to worry about defending Iraq.
Yazdegerd prepared his army, under the command of Rostam Farrokhzad, and ordered it to march out to meet the Arabs, but, sure enough, he just left it sitting there until after the Arabs had won at Yarmouk and could turn their full attention to Iraq. Umar quickly ordered his commanders in Syria to dispatch men to join the army in Iraq, and they sent a force of 5000 now quite seasoned soldiers to the east. Even with those reinforcements, the Arabs were vastly outnumbered, with somewhere around 30,000-35,000 men against a Persian army that may have been as large as 100,000 (though it was probably somewhere between that figure and lower estimates of 50,000). Some sources put the Persian army as large as 200,000+, but that seems extraordinarily excessive (though this was an army raised in desperate self-defense by a very large empire, fighting on its home turf, so if any late antique army was ever going to be that large, it would’ve been this one).
The two armies camped opposite each other for months while talks went on and Umar bought time for his army in Syria to defeat the Byzantines. Later Arab accounts spend as much time recounting these talks as they do on the battle itself, but the accounts can’t be considered accurate portrayals of real events. Many of them were written much later than the events themselves, and even the ones that were written within a relatively short time after those events are so stylized (including accounts of deliberations within the Persian court, featuring full dialogue) that they’re obviously fictional. You read about ragged-looking Arab soldiers being brought to the immaculate, wealthy Persian court, where the Persians attempt to dazzle them with their vast riches to no effect, while the Persians are themselves dazzled by the fighting prowess and/or innate character of the Arab/Muslim warriors. These are obviously stories rather than histories. You see some of the same tropes about the decadent Sasanians as you might find in an ancient Greek account of the decadent Achaemenids, or (interestingly) as you might later about the decadent Caliphal court in accounts of the Mongol conquest of Baghdad in 1258. They are valuable not as accounts of the actual negotiations between the Arabs and Persians, but as accounts of how the Arab conquerors and their descendants viewed the Persian Empire.
Finally, on November 16 (we think), the fighting started. As with the accounts of the Persian-Arab negotiations, we don’t really know very much about the battle because most of what was written about it was written much later and in an episodic, kind of myth-building way (lots of champion-vs-champion fighting, for example). It would be like extrapolating details about the Trojan War, which probably was a real thing that really happened, from reading the Iliad, which is a chronicle of heroic legends about mythic figures and likely was never intended to accurately describe real events. You can get a sense of the contours of the battle, but not the gory details.
It was a four-day affair (maybe; it’s not really a lock that we’re commemorating the right day here, just FYI), and a pretty brutal one, as neither side could really get an edge. The Arabs focused on sidelining and eventually eliminating the Persian war elephant units, which they finally did, sadly at great cost to the elephants (and to the men who got trampled as the hacked-up animals fled). On the second day, the reinforcements from Syria finally arrived, in a continuous stream of small units meant to make it look like there were more of them than there really were in order to demoralize the Persians, but this was not enough to immediately change the course of the battle. At some point near the end of the battle, Rostam was apparently killed in an Arab strike on his command post. The decisive factor, again according to the sources, may have been the superiority of Arab archery and/or armor; their arrows could apparently penetrate the Persians’ armor much more easily than vice versa. There may also have been a sandstorm blowing in the Persians’ faces on the final day, but don’t quote me on that.
Whatever finally caused the Persian army to break, it did break, and the way was open for the Arabs to take the last two prizes left in Persian Iraq. First was the Sawad, the rich alluvial plain between the Tigris and Euphrates Rivers in southern Iraq, which, along with the Nile Valley, became the breadbasket of the caliphate, at least for a couple of centuries until over-farming and over-irrigation began to ruin its soil. Second was Ctesiphon, which fell to the Arabs in March 637. The Persian Empire wasn’t finished yet, but like Carthage after the Second Punic War, it was all over but the shouting. Umar decided to pause the conquests in order to consolidate control over the territories that the Arabs had just won, but when Yazdegerd attempted to reconquer Iraq in 642 (his army was quickly defeated at the Battle of Nahavand), that helped spur a new round of Arab expansion.
Yazdegerd spent the next several years basically running for his life throughout Iran, trying to raise some kind of army. But very few of Yazdegerd’s governors in the east wanted to help him and risk getting on the wrong side of the oncoming Arab armies, and on the rare occasions when he could raise a force it would be quickly defeated. He wound up in the city of Merv, along the Central Asian Persian-Turkic frontier, in about 651. The governor (marzban) there, a guy named Mahuy or Mahuy Suri, wanted nothing to do with Yazdegerd, so he engaged a nearby Turkic tribe to kill him. Yazdegerd supposedly got wind of this plot and tried to flee, but was murdered by what may have been a simple thief (though it’s also possible that Mahuy put the guy up to it) at an oasis outside the city. Yazdegerd’s sons kept running east, eventually ending up in the Chinese court, still claiming to be the rightful rulers of the Persian Empire, but in reality the empire died with Yazdegerd, or at Qadisiyah.
The final end of the Roman Empire, in 1453, was an astonishing event in the sense that there had been a “Roman Empire” of some kind or another in existence for nearly 1500 years, and nearly 2000 years if you go back to the founding of the Republic. The Sasanians weren’t around for nearly that long, but if you go back to the Median Empire of the late 8th century BCE, there was a “Persian Empire” of some kind or another in existence for nearly 1400 years before the Arabs snuffed it out. The conquest of Persia expanded the caliphate dramatically and eventually lent it many of its imperial high-court trappings. The Persian language, in a modified form, eventually became one of the great languages of Islamic civilization, and Persian culture came to define at least the eastern half of the caliphal domains. Oh, and the conquest of Persia also cost one Caliph his life–Umar was assassinated in 644 by a group Persians who were trying to strike a blow against their Arab conquerors.