Texas starter Ryan Dempster (7-6, 2-1 with the Rangers) pitched eight innings, gave up four hits and one run and struck out six. All nine Rangers who stepped to the plate recorded a hit in the game.
Baltimore scored its lone run in the first inning when Adam Jones scored Nate McLouth on an infield single. Texas took the lead with a three-run fourth inning, with RBI singles from David Murphy and Geovany Soto and a sac fly from Ian Kinsler.
Texas extended its lead to 5-1 off an RBI-single from Nelson Cruz in the fifth and an RBI single from Murphy in the eighth.
Orioles starter Miguel Gonzalez (5-3) gave up eight hits, four runs and struck out two.
The second game of the series is scheduled for Tuesday at 7:05 p.m. CT. Scott Feldman will pitch for Texas, while Chris Tillman will take the mound for Baltimore.