Atlanta police spokesman John Chafee said a man died after falling more than 60 feet from an upper-level platform to a parking lot. He said the fall that occurred before 9 p.m. appeared to be an accident.
Hamels (5-13) struck out nine with one walk while allowing six hits and one run as the Phillies snapped a streak of 11 straight road losses.
Asche, a left-handed hitter, pulled a fastball from Julio Teheran (9-6) about three rows deep into the right-field seats in the sixth inning for his second homer.
Phillies manager Charlie Manuel earned his 1,000th career win.
Asche hit his homer two pitches after Teheran hit Darin Ruf with a pitch. Chase Utley, who led off the inning with a single, also scored on the homer.
Asche singled off Anthony Vavaro in the ninth, stole second and scored on a single by Carlos Ruiz.
Hamels didn't allow more than one baserunner in any inning until the seventh, when he walked Dan Uggla with one out after Chris Johnson singled. B.J. Upton then hit into a double play to end the inning.
Upton, who struck out to end the second with Brian McCann on third base following his leadoff double, is 7 for 73 (.096) with runners in scoring position. He's hitting .191 overall.
Justin Upton led off the ninth with a double to left field. With two outs, Chris Johnson hit a ground-rule double to right field to spoil Hamels' shutout bid.
The Phillies took a 1-0 lead in the second. Hamels hit a one-out triple beyond the reach of B.J. Upton in center field and scored on Jimmy Rollins' single. With two outs, Utley singled and Domonic Brown walked, loading the bases, but Ruf's groundout ended the inning.
Teheran gave up four runs on six hits and one walk in six innings, ending his streak of four straight starts allowing no more than one earned run.
McCann returned after sitting out two starts to rest his sore right knee. Justin Upton started after leaving Sunday's game with cramping in his left hamstring.
The start of the game was delayed 1 hour, 48 minutes by rain.
Chafee, the police spokesman, said it was unclear if wet conditions contributed to the fan's fall.
He said police received the report of the fall just before 9 p.m. When officers arrived, they located a man who appeared to have fallen 65 feet, or about six stories.
The man was transported to Atlanta Medical Center and died of his injuries. The man's name was not immediately released.