The Twins' outburst came after the Indians scored five runs in the top of the second for a 5-2 lead.
Joe Mauer hit a solo fifth-inning homer and scored three runs. Eight players had one hit apiece for the Twins, who have won four in a row and eight of 10.
Cleveland's Grady Sizemore had two hits, one a three-run second inning homer. Three others had one RBI, while Andy Marte also had two hits in the Indians' seventh straight loss.
The losing pitcher, after his first blown save, was reliever Tom Mastny (0-2).