Gattis connected for a solo shot off Jeff Francis in the fourth inning, breaking a 3-3 tie, while Justin Upton launched his 10th homer of the season and Dan Uggla provided a two-run shot for the Braves.
Mike Minor (3-1) earned the win, yielding three runs on five hits over six innings. The left-hander struck out five and walked two.
Luis Avilan and Eric O'Flaherty each hurled a scoreless relief frame and Craig Kimbrel racked up his eighth save as Atlanta broke a three-game skid in a contest rescheduled from Monday due to snow and cold.
Francis (1-2) was reached for four runs on six hits over four full frames.
Josh Rutledge, Wilin Rosario and Jordan Pacheco each drove in a run for the Rockies, who dropped the first of a three-game series.
Swim Week Miami Beach 2014 [PHOTOS]