DOHA, Qatar — It seemed a thankless and impossible assignment: negotiating a deal with the Taliban that offers the United States an exit from its longest war.

But Zalmay Khalilzad, the Afghan-born American envoy and architect of the deal, drew on everything he had to pull it off: broad autonomy from his bosses in Washington, nearly four decades of experience in U.S. academia, government and diplomacy, and a lifetime of dealing with tumultuous Afghan politics.