Asche's two-run drive capped a six-run burst in the fourth inning that made it 10-1. He had three hits and fellow rookie Darin Ruf also homered.
Martin (1-1) got more than enough support. He pitched five innings and allowed one run and four hits, striking out four and walking three. Nate Schierholtz homered in the fourth.
Chase Utley delivered an RBI double on the day the Phillies announced a new contract with the star second baseman that goes through the 2015 season.
The Phillies took two of three from the Cubs for their first series win since the All-Star break.
Jeff Samardzija (6-11) was chased in the big fourth. He gave up nine runs and 11 hits in 3 1-3 innings in his shortest outing of the year.
The game was delayed by rain for 22 minutes in the seventh inning.
Ruf got the first of four consecutive Phillies hits in a two-run second inning. John Mayberry Jr. and Michael Martinez each had RBI singles.
Ruf launched a two-run homer in the third, connecting on an 0-2 pitch. It was his second drive of the series and fifth home run of the year.
Carlos Ruiz's bunt single drove in the first run in Philadelphia's fourth. Domonic Brown added a two-run single and Asche hit a line-drive homer to right field.
John McDonald hit his first homer of the year, a two-run shot in the eighth.
NOTES: Phillies 3B Michael Young was in the original lineup but was scratched and did not play. ... Anthony Rizzo doubled for the Cubs. Of his 102 hits this season, over half (52) have been for extra bases. ... The Cubs have an extra-base hit in 31 consecutive games. ... The Phillies claimed OF Casper Wells off waivers Thursday from the Chicago White Sox. ... Thursday's win marked No. 999 for Phillies manager Charlie Manuel in his career. He is on deck to become the 59 manager in major league history to win 1,000. ... Philadelphia embarks on a six-game road trip in Washington beginning Friday, when former Nationals pitcher John Lannan (3-4, 4.10) will start. ... The Cubs will be in St. Louis on Friday to begin a three-game set with the Cardinals. Chris Rusin (1-1, 3.98) will get the ball in the first game.