Cameron Rupp drove in the tiebreaking run with a sacrifice fly and Philadelphia scored four times in the 10th inning for a 6-2 victory over New York.
The Phillies won for only the seventh time in their last 24 games in Queens. They are 13-29 against the Mets since the start of the 2015 season and have lost 15 of the past 17 series between the NL East foes.
Just last week, the Mets swept a three-game series in Philadelphia.
"It was really good to beat these guys," Phillies manager Pete Mackanin said. "We had to change the trend a little bit. Hopefully that gave us some confidence in playing them from here on out."
Odubel Herrera homered early for the Phillies, who took advantage of Reyes' pivotal error and handed the Mets their fourth straight defeat following a five-game winning streak. Slumping badly at the plate this season, Reyes dropped a two-out popup in the eighth when he nearly collided with catcher Travis d'Arnaud along the third base line.
"I have it right there. I just lost the ball. I have to catch that ball in that situation," Reyes said. "We were winning by one run there and that's what happens when you give extra outs to a big league ballclub -- they're going to make us pay."
New York's past five games have been decided in the winning team's final at-bat, including three losses at Miami last weekend, and Mets relievers are 0-4 with a 7.15 ERA during the skid.
Michael Saunders led off the 10th with an infield single that ricocheted off Rafael Montero's foot. Tommy Joseph singled to right field, sending Saunders to third, and Rupp's long fly to the warning track in right gave Philadelphia a 3-2 lead.
Pinch-hitter Aaron Altherr followed Freddy Galvis' single with a base hit of his own, driving in Joseph for the Phillies' fourth run and chasing Montero (0-2). Daniel Nava broke it open against Sean Gilmartin with a two-run single to make it 6-2.
Luis Garcia (1-0) pitched a scoreless ninth for the win.
With two outs in the eighth and Rupp on first base, Galvis hit a fairly routine popup about halfway up the third base line. A drifting Reyes bungled the catch, almost bumping into a stationary d'Arnaud as the ball popped out of his glove.
"That's my ball," Reyes said.
"We'll take it any way we can get it," Mackanin said.
Galvis reached first on the error, with Rupp advancing to third.
"When he dropped it, it was kind of, whoa! It happens. It's one of those things. This game can get you," Rupp said.
Blevins was summoned to face Blanco, who lined a full-count slider well over the head of left fielder Yoenis Cespedes for a ground-rule double.
Wheeler allowed one run in his third start since missing the past two seasons while recovering from Tommy John surgery.
With two outs in the first, Herrera launched a 1-1 curveball into the Mets' bullpen to give the Phillies a 1-0 advantage. New York responded in the bottom half, scoring twice on Jay Bruce's RBI single and a run-scoring wild pitch.
Recalled from Triple-A earlier in the day to replace injured Clay Buchholz, Phillies starter Zach Eflin gave up two runs over five innings in his first outing since undergoing knee surgery last August.
"It's really unbelievable, honestly, just all the hard work I put in this offseason that's led me to this point," Eflin said. "Obviously I wanted to be here more than anything and I got that opportunity."
SETTING THE TONE
Phillies leadoff man Cesar Hernandez (2 for 6) extended his hitting streak to 11 games. He is batting .388 (19 for 49) during the streak.
Phillies: Buchholz had surgery to repair a torn flexor tendon in his right forearm. The two-time All-Star might miss the rest of the season. ... OF Howie Kendrick (right abdominal strain) was placed on the 10-day DL.
Mets: RHP Seth Lugo (partially torn ligament in pitching elbow) and LHP Steven Matz (left elbow inflammation) are both scheduled to begin throwing programs on Wednesday. ... 3B David Wright (neck surgery) is set to resume baseball activities in the next day or two after stopping for a short period due to the flu and some discomfort in his lower back, according to general manager Sandy Alderson.
Two struggling right-handers are scheduled to face each other Wednesday night, with Vince Velasquez (0-2, 9.00 ERA) taking on the Mets for a second straight outing. New York counters with rookie Robert Gsellman (0-1, 9.28).