Sabathia (9-3) hurled his career 34th complete game, yielding a pair of runs on seven hits while issuing just one walk.
He was backed by three RBI from Derek Jeter, whose two-run single in the fifth inning erased a 2-1 Yankees deficit. The New York shortstop added a run-scoring hit in the seventh while Robinson Cano and Mark Teixeira socked solo homers for the Yankees, who lengthened their American League East lead to 2 1/2 games over Baltimore.
The Braves' Mike Minor (3-5) absorbed the loss, surrendering four runs on four hits over 5 2/3 innings, as Atlanta dropped the first of a three-game interleague set.
Michael Bourn went 2-for-4 with an RBI for the Braves, who fell for the seventh time in eight games.