Kurt Suzuki began the rally against Andrew Miller (1-2) with a one-out double. After Chris Parmelee fanned, Hicks' liner to left fell in to give Suzuki enough time to beat the throw to the plate.
Parmelee hit an early two-run homer and Brian Dozier knocked in the other run for the Twins, winners in four of their last six. Brian Duensing (1-1) tossed a scoreless top of the 10th, after closer Glen Perkins allowed two runs in the ninth.
Aaron Hicks' RBI single in the bottom of the 10th inning sent Minnesota past Boston by a 4-3 count in Thursday's rubber match of a three-game series.