BALTIMORE -- The Orioles love to hit home runs, but the Minnesota Twins have shown Baltimore the value of manufacturing runs over the last two games.

Byron Buxton picked a good time to get his first major-league RBI, lining a tiebreaking single to left with two outs in the seventh inning that gave the Twins a 3-2 victory on Saturday night.

Buxton's single, which came off right-handed reliever Brad Brach, capped a two-run, seventh-inning rally against Orioles starter Chris Tillman and right-hander Brad Brach. The rookie center fielder also made a crucial sacrifice bunt in the sixth that set up the first Minnesota run.

The Twins scored their first run in the seventh on catcher Kurt Suzuki's safety squeeze, which set up Buxton's game-winning hit.

"It was a tough game," Twins manager Paul Molitor said. "When you're battling to score runs and trying to find ways to put something together, it's (hard). We had to scratch out some runs."

The Twins did that after Baltimore starter Chris Tillman retired 14 in a row and took a 1-0 lead into the sixth. Shortstop Eduardo Escobar doubled to start the inning and moved to third on Buxton's sacrifice bunt, scoring on second baseman Brian Dozier's single.

Shortstop J.J. Hardy gave Baltimore a 2-1 lead with his sacrifice fly in the sixth before the Twins quickly answered.

Left fielder Eddie Rosario drew a one-out walk off Tillman in the seventh. Rosario went to third when right fielder Torii Hunter singled. Suzuki then dropped a perfect squeeze bunt near the mound that Tillman fielded, but the right-hander could throw only to first as Rosario scored the tying run.

Brach came on and intentionally walked Escobar -- after going 3-0 on the count -- before Buxton lined the tiebreaking single to left, scoring Hunter. The rookie finished the night 2-for-4 and has hits in six of his first seven games.

"Just really blessed and thankful to be able to get my job done and put us in a good position to score and a good position to win as well," Buxton said. "That's baseball to a T. You always want to go up there and get the job done."

Minnesota right-hander Casey Fien (4-5) got a victory for the second consecutive game thanks to 1 1/3 innings of scoreless relief after replacing starter Kyle Gibson, who gave up two runs in 5 2/3 innings.

Right-hander Kevin Jepsen came on in the ninth to earn his second save in two nights as closer Glen Perkins (neck) remains out for a few more days.

The Twins (62-61) have won the first three games of this four-game series and are 6-0 vs. the Orioles (62-60) this season.

Baltimore and Minnesota play the final game of the season series on Sunday, and both teams remain in the thick of the wild-card race.

This was the second consecutive night the Twins rallied to hand the Orioles a tough loss, but Baltimore manager Buck Showalter said his team will continue battling.

"I don't know if there's frustration," he said. "You know how good the competition (is) and you know how good you have to be. It's not like you just throw your gloves and balls out there and things happen. But the last three games have been frustrating for us, especially the last two."

The Orioles took a 1-0 lead in the second. Designated hitter Steve Clevenger stretched his hitting streak to six games with a one-out single to center and scored on left fielder Henry Urrutia's two-out double to left-center, the first two-bagger of his career.

Tillman (9-8) had won his last seven decisions but saw that streak end despite giving up just three runs on four hits in 6 2/3 innings. He said the same thing as third baseman Manny Machado in the locker room: The Orioles simply need to play better. They went 2-for-8 with runners in scoring position and left nine on base.

"We haven't been playing baseball," Machado said. "They've been beating us, outhitting us. In key situations, we haven't been hitting clutch. We've just got to keep fighting."

NOTES: SS J.J. Hardy felt some groin discomfort Friday in a loss to the Twins but still started Saturday after doing all right in his pregame work. He'll probably get a rest day on Sunday, according to Orioles manager Buck Showalter. ...Showalter said INF/OF Steve Pearce's situation will be re-evaluated after this game. Pearce (strained oblique) played his first rehab game at Double-A Bowie and was scheduled to do one more there Sunday and then possibly join the team for the Kansas City/Texas road trip that starts Monday. Showalter said Pearce might need just one game. ... LHP Glen Perkins played catch before the game and did fine. He'll throw a bullpen session Sunday and, if all goes well, be available for duty on Tuesday. ... Newly acquired left-hander Neal Cotts joined the Twins. They got him from the Milwaukee Brewers on Friday for cash or a player to be named. He pitched in 51 games for Milwaukee this year, posting a 1-0 record with a 3.26 ERA.