The unprecedented direct exchanges of fire between Iran and Israel this spring marked a new chapter in the history of Tehran-Tel Aviv tensions. Although the longer-term consequences of the “new rules of engagement” have yet to be realized, there is no doubt that hostilities involving the two arch-rivals have the potential to play out in increasingly unpredictable ways—subjecting the whole region to grave dangers.

While most discussions currently focus on the Iranian-Israeli confrontation playing out in southern Lebanon—where Israel and...