Jesse Crain came on to pitch, and after getting Mark Grudzielanek to line out and fanning Lou Marson, Cabrera lofted a single to shallow left, scoring pinch runner Luis Valbuena with the game-winning run.
Cabrera got two hits and scored a run, Grady Sizemore collected two safeties with an RBI and Peralta also slammed a solo homer in Cleveland's win. Jamey Wright (1-1) registered the win after setting down the final two batters in the top of the 11th.
Denard Span had a good game for the Twins, going 3-for-5 with a home run and two runs scored while Justin Morneau chipped in with a solo shot in the defeat.
Celebrity Families of 2014 [PHOTOS]