Keith Yandle tied it with 12.9 seconds left in regulation and Chris Kreider also scored in regulation for the Rangers, who won consecutive games for just the second time since Nov. 15.
Ryan White scored and Shayne Gostisbehere had a goal and an assist in regulation for the Flyers, who had won three straight. The Rangers improved to 3-2 in tiebreakers this season while Philadelphia dropped to 2-5.
Philadelphia's Sam Gagner shot high and Claude Giroux was stopped by Henrik Lundqvist in the tiebreaker.
New York lost captain Ryan McDonagh midway through the first period when he was knocked out by Wayne Simmonds' punch.
Yandle sent the game to overtime with a blast from the point that rocketed past Steve Mason's left shoulder.
White put Philadelphia ahead 2-1 with 14:14 left in the third period when his wrist shot from the slot beat Lundqvist on the blocker side. The Rangers tied the game 2 1/2 minutes earlier when Kreider deflected Dan Girardi's shot over Mason's left shoulder for his 11th goal.
Gostisbehere put the Flyers up 1-0 with 12:44 left in the second period when he beat Lundqvist with a shot from the point. The goal originally was credited to White, who was filling in for Simmonds on Philadelphia's top power play unit. It would have been White's first power play goal in his 216th career game. Simmonds received a five-minute match penalty and game misconduct for punching McDonagh.
It was the seventh straight game in which Philadelphia has scored on the man advantage. Jakub Voracek also assisted the tally, giving him 11 points (3 goals, 8 assists) in his last six games.
McDonagh crumpled to the ice with 9:24 left in the first period after Simmonds threw a left cross to McDonagh's jaw. Upon the announcement of the penalty, Simmonds hurled his stick on the ice toward the officials before heading up the tunnel.
Simmonds entered on a hot streak, having had six goals and three assists over a five-game point streak that included two goals and an assist in Philadelphia's last game, a 6-3 victory at Nashville on Thursday.
The Rangers went 0-for-2 on the power play, dropping to 2-for-44 in their last 16 games.
Gostisbehere has two goals and eight assists over a seven-game point streak.
The Rangers' only other winning streak since November is the two consecutive games they won on Jan. 19 and Jan. 22.
Notes: Flyers C Sean Couturier (lower body) missed the first game of what is expected to be a four-week absence. Nick Cousins replaced Couturier. ... Rangers D Kevin Klein returned to the lineup two games after fracturing his thumb. ... F Rick Nash (bone bruise left leg) missed his fifth straight game. . Rangers D Dylan McIlrath was a healthy scratch. . Flyers C R.J. Umberger was a healthy scratch for the third straight game.