With two outs in the eighth and the game tied 1-1, Stubbs connected on an 0-1 pitch from Jared Burton (2-7), sending it over the fence in straightaway center field for the decisive blow.
Nick Swisher added an RBI single later in the inning as the Indians took the rubber match of a three-game series and gained ground in the hunt for an American League wild card playoff berth.
Coupled with Oakland's loss to Baltimore Sunday, the Tribe moved within 1 1/2 games of the A's in the wild card chase.
Doug Bernier drove in Minnesota's only run.
Swim Week Miami Beach 2014 [PHOTOS]