Hamels said there's been too much losing in Philadelphia this season to focus on individual milestones.
"Truly I think it hasn't been talked about much in here just because we haven't been playing well," Hamels said. "We've just been focused on just trying to win a game and then going from there.
"It's a tremendous accomplishment. That type of milestone is pretty huge."
The game was overshadowed by a fatal fall at Turner Field.
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.
Philadelphia's players signed a base with "1,000" in Phillies red. The base sat in Manuel's office after the game.
"It's definitely quite an achievement," Manuel said. "Like I told the players, they're the ones who make it happen.
"I'm sure later on it will probably mean a lot more to me than right now."
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.
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.
Despite Hamels' poor record, the left-hander still commands respect in the Braves' clubhouse.
"We know any time we play the Phillies that this could happen with the arms that they run out there," Johnson said. "Give all the credit to Cole Hamels tonight."
Braves manager Fredi Gonzalez said the goal was to get Hamels out of the game.
"We were hoping to get into the bullpen," Gonzalez said. "When you get into those games, sometimes getting into the bullpen helps you the rest of the series. And he didn't let us do that."
Manuel said Hamels showed his determination to remain in the game in the top of the ninth.
"He got his bat and his helmet and made sure he got up on deck real quick," Manuel said. "He was determined he was going to finish."
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.
- The triple was the second of Hamels' career.
- He took his first win in Atlanta since April 20, 2011.
- Manuel is 1,000-824.
- The Phillies' last road win was July 19 at the Mets.
- Braves LHP Paul Maholm, out since July 21 with a bruised left wrist, said his six-inning simulated game before batting practice was a success. Gonzalez said Maholm may need only one minor league rehab game before he can come off the 15-day DL.
- Manuel said he watched on his phone as RHP Roy Halladay threw in the bullpen in Clearwater, Fla. Halladay has been out since May 6 with right shoulder inflammation. "He's looking pretty good," Manuel said.
- Phillies RHP Ethan Martin will face Braves RHP Kris Medlen on Tuesday night.