The game was Americans' last before leaving for the World Cup in South Africa.
Arda Turan put the Turks ahead in the 27th minute on a counterattack after right back Jonathan Spector was dispossessed upfield.
Altidore tied the score in the 58th minute and Dempsey put the U.S. ahead in the 75th, exciting a red-white-and-blue clad crowd of 55,407 at the Linc. The U.S. team took its time leaving the pitch, acknowledging fans at both ends of the stadium.
The Americans leave Sunday for South Africa and meet Australia in a final exhibition on June 5, one week before their World Cup opener against England.
“I think we accomplished everything that we would have wanted here,” U.S. coach Bob Bradley said. “The type of game we were in today pushed them very hard.”
Dempsey was paired at forward with Altidore in the first half, then dropped back to midfield when Robbie Findley replaced midfielder Benny Feilhaber at the start of the second. Findley's speed helped give life to an American attack that lagged, and Landon Donovan played with far more assertiveness in the second 45 minutes to help create both goals.
Bradley said the U.S. responded well to being a goal down, and he wasn't concerned about Donovan. “Landon's experienced and he's smart,” the coach said. “So he's not going to use up all his energy. He's going to read the game.”
When it was time to push, Donovan knew it, he said.
Dempsey nearly got another goal in the 87th, putting an open shot off a post after Michael Bradley cut the ball back.
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