Kinsler came into the game hitting .085 (4 for 47) in his last 13 games, but he hit a two-run homer in the fifth and added a two-run single in Detroit's four-run sixth inning.
JaCoby Jones had two hits and two RBIs for the Tigers in his major league debut, while Todd Frazier homered for Chicago.
Bruce Rondon (5-2) picked up the win in relief of Daniel Norris, who allowed three runs in five innings.
Matt Albers (2-6) took the loss, allowing three runs in the sixth after relieving Anthony Ranaudo.
