Eric Bruntlett, starting at shortstop for the injured Jimmy Rollins, made a diving stop on Carlos Beltran's hard grounder up the middle with two outs in the ninth and runners on first and second, likely preventing the tying run from scoring.
Bruntlett's play helped Brad Lidge escape a shaky ninth for his third save. J.C. Romero (1-0) tossed two scoreless innings for the win.
Feliz led off the seventh with the decisive homer off Pedro Feliciano (0-1) and sent the crowd of 45,173 - the largest of the season - into a frenzy.
Phillies and Mets fans taunted each other all weekend, with finger pointing, derisive chants and even some fights making it feel more like an Eagles-Cowboys game than a late-April series between the NL East rivals.
The Mets fans who made the trip went wild when their team scored four runs in the sixth to tie the game.
Phillies starter Adam Eaton, who had a 5-0 career mark against the Mets, quickly lost his shutout bid in the sixth. Jose Reyes hit a leadoff triple and scored on Luis Castillo's RBI single. David Wright doubled and Carlos Beltran's two-RBI single up the middle made it 4-3 and chased Eaton.
Ryan Church tied the score with an RBI single off reliever Chad Durbin.
That would be all the runs for the Mets, while the Phillies had one more clutch swing left in them.
Utley carried the offensive load and his homers seemed as if they might be enough to carry the Phillies.
He hit a two-out, solo shot in the first off Mike Pelfrey, making him the first Phillie to homer in four straight games since Howard did it at the end of last season.
Pelfrey, who gave up 10 hits and four runs in five innings, threw almost nothing but fastballs. With two on and none out in the fifth, Utley sat on a heater and rocked one off the foul pole net in right. His major league-leading eighth homer of the season made it 4-0, and Utley popped out of the dugout for a quick wave.
The Phillies offense is sputtering without Rollins, who was placed on the 15-day disabled list nearly two weeks after he sprained his left ankle. Rollins hurt his ankle April 8 and had only four pinch-hit appearances and no starts over that span.
First baseman Ryan Howard (.186) is badly slumping and the Phillies have gotten puny numbers from Rollins' replacement, Bruntlett, who was vociferously booed when he grounded into a double play in the second.
Notes: Richard Ashburn threw out the first pitch in honor of his late father, Phillies Hall of Famer and broadcaster Richie Ashburn. The Phillies celebrated the 60th anniversary of Ashburn's major league debut. ... The Phillies observed a moment of silence for former major leaguer and Philly native John Marzano. Marzano died Saturday after falling down a flight of stairs at his home. He was 45. His funeral is Friday morning. ... The crowd cheered when the score of the 76ers' Game 1 win over Detroit was shown on the scoreboard. ... Utley had his 15th career multi-homer game. ... The series drew 135,478, the largest for a three-game series in the five-year history of the ballpark.
