Carroll then lashed a solid single to center field, allowing Span to slide home with the decisive score.
Starter P.J. Walters allowed a first-inning run then fired five shutout frames in Minnesota's victory.
Miguel Cabrera drove in the only run for the Tigers, who blew a chance to forge a first-place tie with American League Central-leading Chicago White Sox with Sunday's two losses.
Instead, the Tigers fell a full game behind the Chisox with 10 contests remaining.
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