Lee (5-2) struck out five, walked two and hit a batter in his first shutout since Sept. 5, 2011. The Marlins were blanked for the ninth time this season.
Lee also helped himself by getting two hits.
Young hit a solo home run off Kevin Slowey (1-5) in the fourth. It was Young's third homer, including a drive off Miami's Jose Fernandez on Tuesday night.
Slowey exited before the sixth inning with a strained left lat muscle. The Marlins said he was day to day.
Slowey allowed six hits and struck out six.
Lee has allowed three or less runs in eight of his 10 starts. Miami's only hits were Marcell Ozuna's infield single leading off the second, Miguel Olivo's lined single opening the sixth and Derek Dietrich's infield single in the ninth.
Philadelphia scored twice off Wade LeBlanc with two outs in the sixth to go ahead 3-0.
Young reached on a two-out infield hit and scored on Domonic Brown's triple. Freddy Galvis singled home Brown.
The Marlins failed to score despite loading the bases with none out in the second. Nick Green grounded into a third-to-home-to-first double play and Jeff Mathis popped up.
In the fifth, Chris Coghlan walked but was thrown out at second as he tried to advance when Green flied out to deep right. Young threw to shortstop Jimmy Rollins, who applied the tag as Coghlan slid in headfirst.
NOTES: Philadelphia 2B Chase Utley is scheduled for an MRI on Thursday on his sore ribcage. He was scratched from the lineup for Philadelphia's 7-3 win on Tuesday night after feeling discomfort during batting practice. ... Miami RF Giancarlo Stanton (strained hamstring) took swings on the field during batting practice for the first time since going on the disabled list April 30. He's hoping to begin running next week. ... The Phillies (23-24) have not been at .500 since being 6-6 on April 14.