The caliph who was running the Arab conquests at that time was also one of those rare geniuses from Moslem history; he planned the entire set of campaigns that conquered Iran, and never left his dining room. But it’s also true that the Byzantines had been getting the better of the Sassanids, and that kinda knees the groin of the “died in the plague” school of thought regarding the decline of the Byzantines. Had they joined forces, the Sassanids and Byzantines might have stopped the Muzzie cutthroats at some battle in Mesopotamia. They did not, or could not, and then it became a piecemeal conquest.
While originally seeming successful at a first glance, the campaign of Khosrau II had actually exhausted the Persian army and Persian treasuries. In an effort to rebuild the national treasuries, Khosrau overtaxed the population. Thus, seeing the opportunity, Heraclius (610–641) drew on all his diminished and devastated empire's remaining resources, reorganized his armies and mounted a remarkable counter-offensive. Between 622 and 627 he campaigned against the Persians in Anatolia and the Caucasus, winning a string of victories against Persian forces under Khosrau, Shahrbaraz, Shahin and Shahraplakan, sacking the great Zoroastrian temple at Ganzak and securing assistance from the Khazars and Western Turkic Khaganate.
In 626, Constantinople was besieged by Slavic and Avar forces which were supported by a Persian army under Shahrbaraz on the far side of the Bosphorus, but attempts to ferry the Persians across were blocked by the Byzantine fleet and the siege ended in failure. In 627-628, Heraclius mounted a winter invasion of Mesopotamia and, despite the departure of his Khazar allies, defeated a Persian army commanded by Rhahzadh in the Battle of Nineveh. He then marched down the Tigris, devastating the country and sacking Khosrau's palace at Dastagerd. He was prevented from attacking Ctesiphon by the destruction of the bridges on the Nahrawan Canal and conducted further raids before withdrawing up the Diyala into north-western Iran.
The impact of Heraclius's victories, the devastation of the richest territories of the Sassanid Empire, and the humiliating destruction of high-profile targets such as Ganzak and Dastagerd, fatally undermined Khosrau's prestige and his support among the Persian aristocracy. In early 628, he was overthrown and murdered by his son Kavadh II (628), who immediately brought an end to the war, agreeing to withdraw from all occupied territories. In 629, Heraclius restored the True Cross to Jerusalem in a majestic ceremony.[56] Kavadh died within months, and chaos and civil war followed. Over a period of four years and five successive kings, including two daughters of Khosrau II and spahbod Shahrbaraz, the Sassanid Empire weakened considerably. The power of the central authority passed into the hands of the generals. It would take several years for a strong king to emerge from a series of coups, and the Sassanids never had time to recover fully.
Heraclius' health was declining when the Arab invasion began so he couldn't lead the campaign or he might have whooped them too.
These two enemies had been fighting for centuries and hated each other, but it is one of the interesting thought experiments in history to think what might have happened had the Byzantines and Sassanians joined forces against the Arabs. Islam would have remained a backwater religion restricted to the Arabian Peninsula.