Right-hander Vance Worley labored through five innings, and Minnesota's offense rallied late but couldn't come through in a 2-1 loss to Texas at Target Field.
Josh Willingham had a prime opportunity to put the Twins ahead in the eighth with the bases loaded and one out, but reliever Tanner Scheppers got him to hit into an inning-ending double play.
"We had our chances," Twins manager Ron Gardenhire said. "When you get Willy in that situation, he hit a bullet but they were playing him there. They pounded him inside but he hit the ball hard, it just ended up being a double play. But it was an exciting ballgame. We were one hit away."
Willingham, who homered off Rangers' rookie starter Nick Tepesch in his previous at-bat, worked a full count against Scheppers but hit a hard grounder to Elvis Andrus for a textbook 6-4-3 double play.
"I hit the ball hard, but I just hit it right at them," Willingham said. "I battled and got a pitch and put the barrel on it, but it just went right at them."
Worley, meanwhile, struggled early, as he needed 52 pitches to get through the first two innings of the game, including 37 in the second inning.
The Rangers got on the board in the second inning with an RBI single from Nelson Cruz to score Adrian Beltre, but Cruz was thrown out by right fielder Chris Parmelee at second base while trying to stretch the hit into a double.
Worley settled down after that, as he didn't give up a run again until the fifth, when Elvis Andrus came through with a two-out RBI double to score Leonys Martin. But it was the final inning for Worley, who surrendered two runs on six hits and two walks.
"I thought everything was coming out of my hand a little up the first couple of innings," said Worley, who fell to 0-3 with a 6.38 ERA. "But then I settled down and everything worked the way I wanted it to. They fouled off a lot of pitches to get my pitch count up, which made it tougher to go deep into the game, but for the most part I'm happy with what I did."
He was outdueled by Tepesch, who didn't allow his first baserunner until Justin Morneau led off the bottom of the fifth with a single.
Tepesch gave up his first run in the seventh on Willingham's team-leading third homer of the year. Parmelee and Trevor Plouffe both singled with two outs in the seventh to chase Tepesch from the game, but left-hander Robbie Ross was able to get pinch-hitter Ryan Doumit to ground out to short to end the inning.
Tepesch, making just his fourth career start, allowed one run on five hits over 6 2/3 innings to get his second career win.
" I felt good about it," Tepesch said. "I kept the team in the game. The guys made a lot of good plays behind me. I didn't feel like anything was extra out of the ordinary, but I felt like I commanded my pitches pretty well. I felt like I was pretty good tonight.
Former Twins closer Joe Nathan threw a scoreless ninth to preserve the victory for the Rangers and pick up his seventh save. But the Twins did get a baserunner with a two-out single from Plouffe before Doumit flied out to deep left field to end the game.
"He's on the other side now, but good memories with Nathan," Gardenhire said. "But we wanted to get him. But he's a closer and bona fide as they say. He made some good pitches."