Placido Polanco slapped an RBI double in the sixth to break a 3-3 tie in Detroit's 4-3 verdict over Texas.
Detroit's bullpen didn't allow a baserunner in four innings of work.
Texas scored two unearned runs in the fifth following errors by third baseman Brandon Inge and shortstop Adam Everett.
Detroit's bullpen, considered a weakness this season, was dominant.
Matt Harrison (0-1) took the loss, allowing four runs, nine hits and five walks in 5 2-3 innings.
"I was pleased with what I did today, but the walks are frustrating," he said. "I was able to keep it close, but I have to have better control."
Hank Blalock homered and Josh Hamilton drove in two runs for the Rangers, who have lost seven straight at Comerica Park.
"We had opportunities all game, and we didn't take advantage of them," manager Ron Washington said. "Our offense hasn't gotten anything going."
The Rangers took a 1-0 lead on Blalock's second-inning homer, but the Tigers came back with two in the bottom half.
With one out, Thames and Gerald Laird singled, and Harrison walked Inge to load the bases. Everett, who came into the game hitting .143, bounced a two-run single between third and shortstop.
The Rangers loaded the bases in the fifth before Hamilton flared a two-run single into left to give Texas a 3-2 lead.
Detroit scored once in the fifth inning when Polanco made the game-winning hit.
Detroit has won the first two games of the series after opening the season by dropping three of four in Toronto and they'll go for a sweep on Sunday.
