Texas' Wayne Tolleson drove in Larry Parrish with a sixth-inning sacrifice fly for the winning run against Seattle in Arlington Stadium.
The Rangers entered the sixth trailing, 4-3, and had not had a hit since the first. Pete O'Brien broke the ice with a leadoff single, Gary Ward grounded into a fielder's choice and Parrish walked, chasing Frank Wills (2-1).
Tommy Dunbar hit a run-scoring single off Ed Nunez and Glenn Brummer's infield single filled the bases for Tolleson's second RBI of the year in 95 at bats.
Chris Welsh (1-1) won with 3 1/3 innings in relief of Dickie Noles. Greg Harris got the final nine outs.
The Rangers used four consecutive hits to take a 3-0 lead in the first. Curt Wilkerson and Buddy Bell singled, O'Brien hit a two-run double and Ward hit a ground-rule double, driving in O'Brien.
Bell's single gave him 1,528 total bases as a Ranger, tying Jim Sundberg's club record.
The Mariners scored four times in the second. Ivan Calderon hit a run-scoring triple and David Henderson, Spike Owen and Jack Perconte hit RBI singles.