Hamels (5-13) notched his first triumph since July 9, a span of six starts during which he compiled a 2.57 ERA but didn't have a win to show for it.
The left-hander broke the spell Monday, however, with his 13th career complete game and first of the year, during which he yielded six hits and a walk while striking nine in a game delayed 2 hours by rain.
Atlanta's Julio Teheran (9-6) took the loss, surrendering four runs on six hits over six full innings.
Chris Johnson drove in the only run for the National League East-leading Braves in the ninth inning, spoiling Hamels' shutout bid.
The game was marred when a male fan fell about 65 feet to his death from a platform at Turner Field during the rain delay.
The man tumbled into a private parking lot at about 8:30 p.m., police told WXIA-TV, Atlanta. He was taken to Atlanta Medical Center, where he was later pronounced dead.