The Brewers had forced extra innings when they tied the score in the eighth on a two-run homer from Aramis Ramirez. Minnesota went back ahead in the 11th when pinch-hitter Plouffe clubbed a two-out solo shot into the Brewers' bullpen off Manny Parra (0-1).
Matt Capps racked up his ninth save with a 1-2-3 ninth, securing the Twins' fourth straight victory.
Jeff Gray (3-0) was credited with the victory with a scoreless 10th inning.
Brian Dozier drove in two runs while Ben Revere and Jamey Carroll each chipped in with two hits and an RBI for Minnesota.
Nyjer Morgan went 3-for-5 with three runs scored for Milwaukee, which dropped its fourth straight and fell for the sixth time in seven games.
2014: The Year in Music [PHOTOS]