Delmon Young led off the ninth with a single against Chad Qualls (3-3) and went to second on Luke Hughes' sacrifice.
After Tsyoshi Nishioka was intentionally walked, Butera hit a grounder into the hole that bounced off the glove of diving Padres third baseman Chase Headley, sending Young home with the game-winner.
Reliever Alex Burnett (2-4) was credited with the victory for the surging Twins, who erased a 3-1 deficit with a three-run seventh inning and won for the 14th time in 16 games.
San Diego starter Dustin Moseley yielded only one earned run on three hits in a 6 1/3-inning effort.
Headley and Ryan Ludwick each stroked a pair of hits and drove in a run in the Padres' loss.