Carlos Santana's pinch-hit home run leading 5 victory over the game series.
Chris Perez (4-7) pitched a perfect top of the ninth inning for the win.
Matt Capps (4-7) gave up Santana's home run on the first pitch he threw in the bottom of the ninth.
"He's trying to get ahead of the guy first pitch," Twins manager Ron Gardenhire said. "You come in ready to hit a fastball when you're pinch- hitting. He threw a fastball over the middle of the plate and the kid killed it."
Jim Thome, who was honored before the game in recognition of his 600th career home run and was informed a statue of him will be placed at Progressive Field, went 3-for-4 with a home run and three RBI.
"That was unbelievable for Jim," Indians manager Manny Acta said. "He's still got that strength, that power."
Chris Parmelee homered and drove in three runs for Minnesota, which lost for the 12th time in 13 games.
Carl Pavano allowed five runs on 10 hits and a walk through a 6 1/3-inning start for the Twins. Justin Masterson started the game for the Indians, allowing four runs -- three earned -- on five hits and six walks through 4 2/3 innings.
Ben Revere led off the game with an infield single and was followed by a Trevor Plouffe walk. After Michael Cuddyer's groundout to first moved the runners to second and third, Parmelee sent a base hit up the middle to bring Revere and Plouffe across the plate, giving the Twins an early two-run advantage.
Cleveland answered with a run in the bottom of the frame when Kosuke Fukudome singled, moved to second on Jason Kipnis' groundout to first and scored on Thome's double off the wall in left.
The Indians then tied the game in the second. Lonnie Chisenhall singled and came around to score on Matt LaPorta's double to right-center that landed just out of the reach of a diving Revere.
But Parmelee's leadoff home run in the third put the Twins back on top. With runners on first and second and one out later in the frame, Joe Benson hit a grounder to third. Chisenhall threw to second for the force, but Kipnis' throw to first was low and bounced past the bag, allowing Brian Dinkelman to score on the throwing error and giving Minnesota a 4-2 lead.
Cleveland answered again in the home half of the third with a two-run shot over the center-field wall by Thome. Kipnis walked prior to Thome's 15th homer of the year.
Luke Hughes and Dinkelman worked walks before Rene Tosoni was hit by a pitch to load the bases with no outs in the fifth. Benson stepped up next and hit a bouncer right back to the mound that Masterson fielded and threw home for a 1-2-3 double play. Drew Butera walked to load the bases again and Masterson was pulled in favor of Frank Herrmann, who induced a Revere pop up to the catcher to end the inning and keep the game knotted at four.
Chisenhall doubled into right-center to lead off the home sixth and came home on LaPorta's base hit to center to put the Indians ahead, but doubles by Hughes and Tosoni in the seventh tied the game at five.
Revere extended his hit streak to 10 games...Thome extended his hit streak to eight games...Tosoni was thrown out at home in the seventh inning...The Indians have homered in 13 of their last 15 games...Minnesota fell to 6-9 against Cleveland this season and has dropped six straight to the Indians.