Mitch Garver and Alex Kirilloff each doubled twice as the Twins cranked out eight extra-base hits to win their third in a row.
Jose Berrios (5-2) allowed one earned run on seven hits, striking out seven in 5 2/3 innings. Taylor Rogers got four outs for his third save.
Cedric Mullins and Maikel Franco each had two hits and DJ Stewart homered for the second night in a row for the Orioles.
Dean Kremer (0-5) gave up five runs on six hits with three walks over four innings. He also threw a pair of wild pitches that scored runs.
The Orioles took a 2-0 lead in the second with a pair of unearned runs. With one out and a runner on first, Ryan Mountcastle hit a chopper to the right of the mound. Berrios fielded it and made an off-balance but on-target throw to second that shortstop Andrelton Simmons dropped for an error.
A two-out walk loaded the bases, and Mullins followed with a two-run single.
The Twins countered with four runs in the bottom half. Polanco got it started with a leadoff homer, Refsnyder doubled home the tying run and after two walks filled the bases, Kremer threw a pair of wild pitches to score two more runs.
The Orioles cut the lead to 4-3 in the fourth when Stevie Wilkerson and Pedro Severino led off with back-to-back doubles, but Berrios retired the next three hitters to end the threat.
Minnesota got that run back in the bottom half when Refsnyder doubled and scored on Josh Donaldson's sacrifice fly.
Kiriloff's RBI double in the sixth put Minnesota on top 6-3.
Stewart and Refsnyder hit solo homers in the eighth inning.
Orioles: RHP Dillon Tate (hamstring) started a rehab assignment Tuesday at Triple-A Norfolk. Tate hasn't appeared in a game since May 7.
Twins: Max Kepler was back in lineup as the designated hitter after missing Monday's game with a sore hamstring, but DH Nelson Cruz (wrist) and utility man Luis Arraez (shoulder) remained sidelined.
In Wednesday afternoon's series finale, RHP Michael Pineda (2-2, 2.79 ERA) is scheduled to start for the Twins against RHP Jorge Lopez (1-5, 6.00). Pineda missed a turn in the rotation after having an abscess removed from his thigh. Lopez allowed two runs and struck out eight over five innings in his last appearance, a loss to the Nationals on Friday.
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