After being shut out for five innings, the Rangers finally broke through against Enrique Gonzalez, the sixth Tigers pitcher, in the top of the 14th.
Gonzalez (0-1) issued a one-out walk to Josh Hamilton and one out later Cruz drove an opposite field blast just fair into the right field stands, handing the first-place Rangers their fourth win in five games coming out of the All-Star break.
Cruz finished 3-for-6 with four RBI and Ian Kinsler homered and drove in three runs for Texas, which snapped an 11-game losing streak at Comerica Park.
Matt Harrison (2-1) got the victory for hurling four shutout innings and Neftali Perez collected his 25th save with a scoreless bottom of the 14th.
Miguel Cabrera belted two homers, went 3-for-6 and drove in three runs for the Tigers, who dropped their sixth straight game.