Hamels (12-6) retired 13 of the first 14 Braves batters he faced and didn't allow a runner to reach second base in the dominating performance -- his fifth career shutout and first since 2009.
The left-hander didn't allow a walk and struck out six while breaking a personal three-game winless streak.
Howard's blast in the first inning followed a run-scoring double by Domonic Brown and handed the Phillies a 3-0 lead.
Mike Minor (6-8) was saddled with the loss, yielding three runs on seven hits over seven full frames for Atlanta, which came into the contest tied with Pittsburgh for the National League wild card lead.
Moore to attend retreat in to avoid Kutcher's wedding
Lytro unveils camera that can focus a photo after shooting it