New York improved to 9-4 against the Phillies this year, after going 6-12 against them last season and losing the final eight meetings.
Eric Bruntlett, subbing for Jimmy Rollins, had three hits for the Phillies, who rallied for an 8-6 win in the series opener against New York but struggled to score after that.
Rollins was a late scratch from the starting lineup - the Phillies didn't immediately announce a reason - and grounded out as a pinch hitter with a runner on to end the game.
Wagner earned his 26th save after missing the opener with a sore left shoulder.
Delgado hit a two-strike pitch from J.C. Romero (4-3) with two outs in the eighth inning into the left-field corner to drive in Robinson Cancel and David Wright, who was intentionally walked before the big first baseman came to the plate.
Left-handed hitters were 5-for-68 (.074) against Romero this season before Delgado's clutch hit, which made the slugger 3-for-18 lifetime against the Phillies' reliever.
Perez fired a called strike past Bruntlett at 12:10 p.m. in the unusual early start. Sections of summer-camp kids provided streaks of color in the upper deck of Shea Stadium, and construction workers at new Citi Field watched a few innings from beyond the center-field wall.
The kids and workers in hard hats were treated to terrific pitching performances by the 26-year-old Perez and 45-year-old Jamie Moyer.
Perez ran his scoreless streak against Philadelphia to 24 1-3 innings before Jayson Werth led off the seventh with a long drive to center that hit the top tier of a camera tower. His 13th homer of the season tied it at 1 and was just the fourth earned run allowed by Perez in his last four starts.
Perez departed after hitting Ryan Howard with a pitch to load the bases with two outs in the eighth. The left-hander ran off the mound - his usual custom - as the crowd saluted him with a long ovation.
Aaron Heilman (1-3) came in and got Werth to fly out to center to end the inning.
Moyer retired eight of his first nine batters before running into trouble in the third, hurt by an uncharacteristic lapse in control. Jose Reyes walked with two outs and stole second. Moyer then walked rookie Nick Evans and Wright lined his next pitch into left for an RBI single.
Evans went to third on Burrell's throw into the infield, but Moyer got Delgado to ground out to second to end the inning.
Moyer set down 13 of the last 14 hitters he faced and allowed one run and two hits in seven innings.
