Jason Michaels singled to center with one out in the 11th off John Franco (0-1) before taking third on a single to left field by Marlon Byrd. Polanco, who had three hits, followed with a deep fly to left to snap a 2-2 tie.
"I really don't want to talk about me because I come here every day and do my job," Polanco said. "I just happened to get the hits today. We've been keeping the pieces, working together, playing solid fundamentals. That helps make our own luck."
Jose Mesa (4-5), the fourth Philadelphia pitcher, tossed two scoreless innings for the win.
Tom Glavine, the Mets' starting pitcher on Sunday, was used as a pinch hitter in the 11th because New York was out of healthy position players. Glavine grounded out to end the game.
The Mets left 10 on base, stranding runners at third in the fifth, sixth and seventh innings, en route to their sixth straight loss. New York needs a victory Sunday to avoid the fourth winless homestand of at least seven games in franchise history.
"Rollins was awesome today," Phillies manager Larry Bowa said. "The key play was him picking up the ball in the outfield, nailing his guy, instead of letting the outfielder make the play."
Mets starter Jae Weong Seo allowed two runs and seven hits in six innings. "Seo actually pitched real well today. I really had to work at the plate," Thome said.
The Mets' first-inning troubles continued when the Phillies scored a run on consecutive doubles by Polanco and Thome. New York has allowed first-inning runs in each of the first six games of its homestand, including nine in the first three games of this series. "I really don't have a problem with it, but we did talk behind closed doors about that stuff," Mets manager Art Howe said of the first-inning woes. "It's more frustrating for the game as a whole, not just the first inning."
The Mets answered in the bottom of the first when Jeff Duncan, who was called up from the minors Thursday, hit his first major league homer.
Houston homered in the sixth to give the Phillies a 2-1 lead.
Phils starter Brandon Duckworth, who is winless in his last eight starts, allowed one run and five hits in 5 1/3 innings. "I didn't have good stuff today, but I gutted it out and we found another way to win," Duckworth said.
The Phillies failed to score in the 10th, despite a leadoff double by Thome.
Reyes tied a career high with three hits and his relay throw nailed Rollins at the plate to end the top of the sixth.
The series ends Sunday with Brett Myers (9-6, 3.61) going against Tom Glavine (6-9, 4.83).