As far as I know Zoroastrian Persia was taken over so quickly by the newborn Caliphate because it had lost the thirty-odd year war against the Roman Empire, rendering it economically weak and leaving its people with less and less faith in their corrupt ruling and priestly classes.
If Chosroes II manages to defeat Heraclius, or perhaps you can have an even earlier POD where Phocas stays in power longer with anarchy in the Roman government coming with it, Persia is in a much stronger position, holding Syria, Egypt, Armenia, and perhaps even much of Anatolia.
Now the Arabs will burst out of Arabia, probably taking Syria and Egypt as in OTL, but unable to penetrate the vast, victorious Persian armies in Mesopotamia and Persia, in the highest fettle after defeating the Romans. So they turn west, taking the north African coast and Spain as in OTL, and having even more resources against the Franks through Spain and the Byzantines through Anatolia.