The Iranian turn has come at an opportune time for Turkish foreign policy in other ways, too. Iran has influence with Iraq’s Shiite-led government and Syria’s Alawite elite. In Iraq, where a crucial oil deal hangs in the balance, Turkey needs Iranian cooperation. It also needs Iran’s help on Syria.

Turkey initially tied its policy to America’s demand that President Bashar al-Assad quit. It was disappointed when the Obama administration signed on to a Russian-brokered deal with Mr. Assad on chemical weapons. With violence menacing across the border, Turkey wants to see an end to Syria’s civil war. The new moderate government in Tehran is Turkey’s best hope for leveraging a settlement.

Economic ties between Turkey and Iran have been strengthening, with trade now estimated to be worth $20 billion. The real number may be still higher, since the recent corruption charges allege that Turkish officials and the state-owned Halkbank have been helping Iranian businesses dodge international sanctions. In any case, Iranian exports still reach Turkey, and the proceeds fund the purchase of gold and silver that flow back to Iran. In turn, Turkey’s economy depends on Iran’s oil and gas, its investments dollars and large export market.