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.