Marlon Byrd, David Wright and Daniel Murphy each had an RBI single for the Mets, who handed Cole Hamels his latest defeat and snapped Philadelphia's seven-game winning streak at Citi Field. Another rookie, Juan Lagares, had a run-scoring single among his three hits.
Jimmy Rollins hit a leadoff homer, and Chase Utley had a two-run shot in the ninth for the Phillies. They put the potential tying run on second with two outs before Bobby Parnell retired Darin Ruf on a game-ending liner to second.
Germen (1-1) escaped a bases-loaded jam and struck out three in 1 2-3 hitless innings for his first major league win.
The series finale Sunday features a marquee matchup of All-Star pitchers: Mets ace Matt Harvey against lefty Cliff Lee.
Wheeler wiggled out of early trouble in his sixth major league start, but New York's prized right-hander needed 106 pitches to get through 4 2-3 innings in 93-degree heat.
Hamels (4-12) allowed three runs in a 35-pitch first inning and was pulled for a pinch-hitter after five. The three-time All-Star and 2008 World Series MVP leads the NL in losses.
Hamels has always had trouble with the Mets. The left-hander, who was 2-0 with a 1.57 ERA in three previous July starts, dropped to 6-12 in 24 outings against New York.
Coming off a gem in San Francisco but pitching for the first time in 10 days, Wheeler gave up a two-strike single to Hamels to start the fifth. The Phillies loaded the bases with nobody out, but all they managed was Utley's sacrifice fly.
All-Star slugger Domonic Brown flied out on a 3-0 pitch, and Wheeler was lifted - one out short of qualifying for a win - after walking Ruf to load the bases again.
Wheeler kept his back to Terry Collins as the manager marched to the mound, then handed over the ball and disappeared down the dugout runway. Collins followed moments later, and Wheeler was back on the bench to greet Germen with a high-five after he struck out streaking Delmon Young to preserve a 3-2 lead.
In his only other outing at home, the 23-year-old Wheeler was beaten by Washington 13-2.
Wright hit a run-scoring single in the fifth, and Murphy added his RBI single in the seventh. LaTroy Hawkins worked the eighth, and Parnell got three outs for his 18th save despite allowing Utley's homer.
Still struggling to command his lively pitches and get ahead, Wheeler has however shown the ability to bear down in a jam. He held Philadelphia hitless in five at-bats with runners in scoring position, leaving opponents 4 for 32 (.125) in those situations during his brief big league career.
Rollins drove Wheeler's third pitch to right for his 45th career leadoff homer, breaking a tie with Brady Anderson for fourth place in major league history.
It was Rollins' first home run in 162 at-bats since May 31. He has a 16-game hitting streak against the Mets.
New York came right back in the bottom of the first with the help of two walks by Hamels, who issued one free pass over 23 innings in his previous three starts combined. Byrd lined a run-scoring single, Lagares fisted an RBI single into shallow right, and Anthony Recker knocked in another by beating out a double-play ball after third baseman Michael Young double-clutched.
New York stole two bases against Hamels, who also picked off a pair of runners.