Rene Tosoni hit a go-ahead homer off of Tony Sipp (6-3) in the tenth, and Minnesota added another run before Joe Nathan closed the door on Progressive Field for 2011 with his 14th save.
Kyle Waldrop earned his first major league win for the Twins.
Each team scored twice in the first, with Lonnie Chisenhall collecting two RBIs with a single scoring Jason Kipnis and Travis Hafner.
The Indians then took a 4-2 lead in the bottom of the third on Shelley Duncan’s 11th homer of the season, but the Twins scored one in the fifth and one in the sixth off of Indians’ starter Fausto Carmona.
After Carmona left in the seventh, Rafael Perez, Vinnie Pestano and Joe Smith got the game to extra innings before Sipp gave up the game-winning runs for the Twins.
Now the Indians head to Detroit to face the Tigers in the final series of the season for The Good Guys. Cleveland leads the White Sox (who lost today to the Royals) by three games, and will only fail to finish second in the Central Division if they lose their last three games and Chicago sweeps the Blue Jays.
If the Tribe wins two-of-three in Detroit they will finish above .500.