Lee (5-2) struck out five, walked two and hit a batter in his first shutout since Sept. 5, 2011.
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"I know I got lucky early in the game with the bases loaded and nobody out, getting the double play there," Lee said. "I felt like I got better as the game went on, too."
The Marlins failed to score despite that threat in the second inning. Nick Green grounded into a third-to-home-to-first double play and Jeff Mathis popped up.
"I was willing to sacrifice a run right there for two outs," Lee said. "Luckily, he hit it to third base where we could get the guy at home and then throw to first, so that was huge."
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.
The Marlins were blanked for the ninth time this season.
"We had that one opportunity to score and didn't get it done and that was about it," Miami manager Mike Redmond said.
Lee also got two hits.
"It's the funnest part of the game for me," he said. "Anytime I can do anything to help the team win, I try to take it serious."
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.
"I feel like I'm ready in time and I'm able to recognize the pitch early," Young said.
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.
Philadelphia scored twice off Wade LeBlanc with two outs in the sixth to go ahead 3-0.
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.
After the game, the Phillies announced RHP Phillippe Aumont was being sent to Triple-A Lehigh Valley. Philadelphia will add a player on Friday to take Aumont's spot. ... 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 hopes to begin running next week. ... The Phillies (23-24) have not been at .500 since being 6-6 on April 14.
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