The Phillies had three two-run innings but it was the six-run fourth that ended all doubt about the outcome of the game.
Asche doubled and scored in the second inning, singled after a two-run home run by Darin Ruf in the third and finished off the six-run fourth with a homer into the seats beyond right field.
Phillies starter Ethan Martin (1-1) allowed four hits and one run -- a fourth-inning home run by Nate Schierholtz -- while walking three and striking out four. It was his first win in the majors.
Philadelphia pounded Chicago's Jeff Samardzija (6-11) for 11 hits and nine runs in 3 1/3 innings.
Ruf singled and Asche doubled to set up run-scoring hits by John Mayberry and Michael Martinez in the second innings and Ruf hit his fifth home run of the year to score Chase Utley for a 4-0 lead the next inning.
Carlos Ruiz, Utley and Dominic Brown, driving in two, had run-producing hits before Asche hit his home run in the fourth.
John McDonald connected for a two-run home run -- his first of the season -- in the eighth for the final runs.