Ryan Howard and Pedro Feliz homered for the Phillies, who scored twice in the eighth off struggling setup man Aaron Heilman to tie it at 3 and spoil a strong outing by Mets starter John Maine.
With two outs in the 12th, Reyes doubled off Tom Gordon (0-2) and Pagan grounded a sharp single to center for his third hit.
Jayson Werth's strong throw home made it a surprisingly close play on the speedy Reyes, who slid around catcher Chris Coste and appeared to touch the plate with his hand just before Coste applied the tag.
Plate umpire Ted Barrett immediately signaled safe, and Phillies manager Charlie Manuel popped out of the dugout for a brief argument as the Mets celebrated nearby.
Rollins was missing from the starting lineup for the second consecutive game because of a sprained left ankle. He struck out as a pinch hitter against Billy Wagner leading off the ninth.
Mets reliever Scott Schoeneweis entered to boos with two on in the 11th, then got Chase Utley to ground into an inning-ending double play and gave a huge first pump as he walked off the mound.
Jorge Sosa (1-0) retired Feliz with one pitch in the 12th to earn the win.
The Phillies rallied and played errorless ball one night after a sloppy performance without Rollins. Eric Bruntlett filled in at shortstop again after making two of Philadelphia's four errors Wednesday night - both in a six-run third inning.
With two on in the 11th on Thursday, Bruntlett struck out trying to bunt.
Maine took a 3-0 lead into the seventh before giving up a leadoff homer to Feliz, his first with the Phillies, and Coste's double off the left-field fence.
Pedro Feliciano pitched New York out of a jam with three straight strikeouts, but Heilman squandered the lead in the eighth.
Howard opened the inning with a 450-foot shot to center, his second home run of the season. Pat Burrell walked and pinch-runner So Taguchi went to third on Geoff Jenkins' single to right. Feliz drove in the tying run with a slow groundout before Heilman escaped further damage.
Ryan Church's two-run single with two outs in the fourth put New York ahead, and Carlos Beltran added an RBI single off Adam Eaton in the sixth. Pagan also doubled and scored twice.
Both starters have a history of shutting down Thursday night's opponent.
Eaton is 5-0 with a 2.90 ERA in eight starts against the Mets, including 4-0 with a 3.08 ERA in six starts at Shea Stadium.
Maine is 4-0 with a 2.05 ERA in seven starts against Philadelphia.
Eaton gave up three runs and five hits in six innings, while Maine yielded one run and five hits in six-plus innings.
