Gerrit Cole (12-7) earned the win with four hits, four runs, three walks and eight strikeouts in five innings.
Eloy Jimenez had three hits, including a two-run home run, and drove in three runs.
Willi Castro hit a two-run homer and Javier Baez had a solo shot for the Tigers.
Rays 5, Rangers 3Christian Bethancourt and Jose Siri hit back-to-back homers in host Tampa Bay's win over Texas.
The duo went deep in the second inning for a 2-1 lead that the Rays never relinquished.