Lonnie Chisenhall went 3-for-4 with two 6, in the opener game series.
Ubaldo Jimenez (4-2) allowed three runs -- one earned -- on five hits over 6 1/3 innings to grab the win. He walked three and struck out four.
Jim Thome and Carlos Santana both hit a solo home run for the Indians, who halted a three-game skid. Despite the win, the Indians were officially eliminated from the AL Central race due to the Tigers' division-clinching victory over the Athletics on Friday.
Kevin Slowey (0-6) surrendered five runs on seven hits over four innings to suffer his career-high sixth straight loss.
Revere went 2-for-4 with two RBI for the Twins, losers of six in a row and 11 of 12.
Thome, who spent last season and parts of 2011 with the Twins before being acquired by the Indians, was treated to a standing ovation after giving Cleveland a 7-4 lead in the top of the ninth with a solo shot.
The home run proved the difference, as the Twins got to Perez in the home half. Consecutive one-out doubles by Joe Benson and Matt Tolbert placed runners at second and third. Revere's groundout scored Benson and Plouffe's single capped the scoring before Rene Tosoni went down on strikes to end the game.
"I was not happy for him," said Twins right fielder Michael Cuddyer. "I mean obviously he was a great teammate, great guy, but he's playing for the other team and that home run ended up being the difference in the game."
Santana gave the Indians an early lead with a homer in the second and Kosuke Fukudome made it a 2-0 game with a run-scoring double play groundout an inning later.
Chisenhall's two-out single plated Thome in the third before Lou Marson's two- run single up the middle put the Indians on top 5-0.
The Twins finally broke through in the fifth when Indians center fielder Grady Sizemore dropped a fly ball off the bat of Tosoni, allowing two runs to score.
Chisenhall responded with an RBI single off of Phil Dumatrait a half-inning later.
Benson's first career triple began the Twins' seventh. Tony Sipp relieved Jimenez two batters later and Revere greeted him with an RBI single. Sipp's errant pickoff attempt allowed Revere to reach third and Plouffe's sac fly made it a 6-4 game.
"Getting a chance to come here and play here for two years, it was very special," said Thome.
Twins designated hitter Jason Kubel was removed from the game with a left foot injury. He was replaced by Tosoni...On Friday, the Twins announced that catcher Joe Mauer will likely miss the remainder of the season with mild pneumonia.