Stewart held off Jimmie Johnson and Clint Bowyer after an accident involving David Ragan and Kurt Busch set up the shootout. Stewart pulled away to gain the 39th win of his Sprint Cup career and second victory of the season.
Chase for the Championship points leader Johnson extended his lead over second-place Denny Hamlin to 36 with his third-place finish Sunday.
Bowyer barely edged out Johnson for second place, while Stewart moved from 10th to fifth place in the Chase rankings, 107 points behind Johnson.
Engine failures were encountered by Kyle Busch, Matt Kenseth and Greg Biffle, spelling probable ends to their championship hopes.