The Twins were trailing 4-3 in the seventh when they started a comeback against Astros reliever Lucas Harrell (5-12).
Clete Thomas led off the inning with a double, moved to third on a sacrifice by Doug Bernier and scored the tying run when Brian Dozier sliced a pitch down the right-field line for an RBI two-bagger.
Oswaldo Arcia capped the rally with a bases-loaded walk as Minnesota clinched its three-game series.
Brett Wallace homered while Robbie Grossman added two hits with an RBI for Houston.
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