The Rangers jumped out to a 7-0 lead in the fourth inning and held on for a 7-5 win over the Tigers in Detroit.
Joey Gallo and Ronald Guzman hit two-run homers to lead the Texas attack.
Yovani Gallardo got the win and Keone Kela his 21st save.
Matthew Boyd gave up all seven runs in four frames to take the loss.
Niko Goodrum homered for Detroit, which has lost three in a row and 14 of its last 16 games.
The Tigers and Rangers play the second of their four-game series tonight at Comerica Park.
Jordan Zimmermann is slated to start for Detroit and 45-year-old Bartolo Colon for Texas.
The Tigers are third in the AL Central at 38-and-51, 12 games behind the first-place Indians.