Santana (10-6) allowed just five hits and matched his career high with 11 strikeouts. Craig Kimbrel struck out the side in the ninth for his 32nd save.
Gattis led off the seventh with a drive into the left-field seats off Jason Lane (0-1), a 37-year-old former outfielder making his first big league start as a pitcher.
Called up from Triple-A to fill in for ailing Ian Kennedy, Lane shut down the Braves through six innings. But when the left-hander hung an 0-1 breaking pitch, Gattis hit his 17th homer of the season and first since June 18, before he went on the disabled list for nearly three weeks with a bulging disk in his back.
