Shane Victorino had three hits, including a home run, and two stolen bases to help the Phillies move within five games of the division-leading Mets.
"We needed to win, everyone knew that," Phillies manager Charlie Manuel said. "The series had been tough on us, but we got a win. Now, it's time to move on to the next series and try to carry the momentum."
Carlos Delgado homered for New York, which had its four-game winning streak snapped. The Mets are 8-2 in their last 10 games.
Because of injuries to starters Freddy Garcia and Jon Lieber, and a doubleheader on Friday, the Phillies' weekend rotation against the Mets included three pitchers who had been in the minors three weeks ago.
Unlike J.D. Durbin and J.A. Happ, Kendrick (3-0) managed to shut down a potent Mets lineup. He gave up two runs and six hits in a career-high 6 2/3 innings. Kendrick walked three and didn't strike out a batter.
He was aware of the dire need for a victory, but kept his composure.
"I didn't try to put any more pressure on myself than there already was," Kendrick said.
J.C. Romero recorded the final out of the seventh and Brian Sanches pitched a scoreless eighth. Mike Zagurski notched two outs in the ninth before pinch-hitter Ruben Gotay hit an RBI single off Antonio Alfonseca, cutting it to 5-3.
Alfonseca then retired pinch-hitter Julio Franco on a grounder for his sixth save in seven opportunities.
Rollins provided the big hit off starter Mike Pelfrey (0-6) in the third inning. The shortstop was 1-for-14 in the series before his 14th homer gave the Phillies a 3-1 lead.
Kendrick received plenty of support from his defense. The Phillies turned three double plays, including one on speedy Jose Reyes in the fifth.
"The double plays killed us," Mets manager Willie Randolph said. "We could have put a lot more pressure on (Kendrick). I don't know the kid, but give him credit, he got through the jams he was in."
New York took a 1-0 lead in the first when Reyes singled, stole second and scored on Paul Lo Duca's single.
New York pulled to 3-2 in the fourth on Delgado's 13th homer.
Pelfrey was recalled from Triple-A New Orleans for Sunday's start when Oliver Perez was scratched because of a stiff back. To make room for Pelfrey, the Mets placed starter Jorge Sosa on the 15-day disabled list with a strained left hamstring.
Pelfrey yielded three runs -- two earned -- and four hits over five innings. As was the problem in his first stint with the Mets this season, Pelfrey struggled with his control. He walked three, including Burrell twice.
"The first time up I was too much of a finesse pitcher," Pelfrey said. "I'm supposed to be a power pitcher. So I just let everything go. I got back to throwing hard.
Randolph was impressed with the new Pelfrey.
"His pitch count (103) was high, but I thought he did a pretty good job," Randolph said.
- Philadelphia 76ers first-round draft pick Thaddeus Young threw out the ceremonial first pitch. Young, out of Georgia Tech, was the 12th player selected in Thursday's NBA Draft.
- Pelfrey recorded his first major league hit with a single in the fifth inning.
- Delgado's 420th homer tied him for 39th on the career list.
- Alfonseca is 1-0 with six saves and a 1.50 ERA in 13 games since Brett Myers went on the disabled list.