Ian Kinsler added a two-run triple in the eight-run first frame, and the Rangers banged out 17 hits en route to their 12th win in 14 contests to start the season.
Nelson Cruz and Mitch Moreland added two RBI the defending American League champions.
Matt Harrison (3-0) earned the victory, yielding three runs on six hits over 7 2/3 innings. He didn't issue a walk and struck out six.
Tigers starter Rick Porcello (1-1) was raked for nine runs (eight earned) on 10 hits in only one inning of work. The Detroit right-hander's ERA rose to 6.32 after the beating.
Miguel Cabrara went 3-for-4 with a two-run homer for American League Central-leading Detroit.