Sabathia (14-6) snapped a personal three-game losing streak with his 10th consecutive win over the Twins. He struck out 10 and walked one.
He allowed both Minnesota runs, with Matt Carson singling in a run in the second inning and Pedro Florimon Jr. getting an RBI in the seventh.
The Yankees scored eight runs between the Twins' scores and beat reliever Brian Duensing (4-11), who was charged with six runs on five hits and two walks in a one-inning appearance. He struck out one.
Duensing came on when starter Samuel Deduno was injured in the second inning. Duensing got the third out in the second and the first in the third but the next seven New York batters reached base.
Chris Dickerson had a two-run shot into the seats beyond right field in the sixth for his second home run of the season.