The Flyers (31-24-6) now trail the Rangers (33-25-3) by one point; each team has 21 games remaining.
Philadelphia lost to the San Jose Sharks 7-3 Thursday in its first game after the NHL break for the 2014 Sochi Olympics.
''I think our guys have good character,'' Flyers coach Craig Berube said. ''I was pretty confident we'd come out and play hard. … They're a fast, hard-working team, and if you want to compete with them you need to play a fast, hard game.''
Wayne Simmonds gave the Flyers a 3-2 lead in the second period less than two minutes after the Rangers tied the score. On a power play, Simmonds' attempted pass deflected back to him and he turned around at the left faceoff dot to send a wrist shot far-side past Rangers goalie Henrik Lundqvist at 13:23.
Lundqvist, playing his first NHL game since winning a silver medal with Sweden at the Olympics, made 27 saves. He had won five in a row and seven of eight, and was 12-2-0 in his past 14 games against the Flyers.
''I read a high shot and he went five-hole,'' Lundqvist said of Simmonds' goal. ''I thought I was patient on the shot; he just beat me. I thought overall we played a really good game and created a lot of good chances. Disappointing, obviously, but I thought we did a lot of good things.''
Flyers goalie Steve Mason, pulled from and reinserted into the game Thursday, made 33 saves.
Philadelphia scored twice in a 1:06 span in the first period after killing off two power plays in the first six minutes.
"We had a couple chances on the power play there that we don't score on, and I think anytime as a team if you get two kills pretty early on in the game you're going to grab the momentum," New York captain Ryan Callahan told MSG Network. "Our first period wasn't where it needed to be, and it seems like we were kind of playing catch-up after that."
A shot by Simmonds was deflected by Vincent Lecavalier and it trickled away from Lundqvist toward the goal. While Brayden Schenn was swiping at the puck, it went in off the stick of Rangers defenseman Anton Stralman at 7:04.
Sean Couturier followed at 8:10 off a partial breakaway after two long passes. Flyers defenseman Kimmo Timonen sent the puck from behind his net through two Rangers forecheckers to Matt Read on the left-wing boards in the neutral zone. Read sent a cross-ice pass to Couturier entering the offensive zone. He skated around Chris Kreider across the goal mouth and put a forehand over Lundqvist, who was on his stomach after missing a poke check.
The Rangers rallied to tie it 2-2 on second-period goals by Kreider and Derick Brassard.
Kreider finished a fast-moving play at 4:59. Derek Stepan sent a cross-ice pass off the right-wing boards, where it bounded to Rick Nash, who in one motion pushed it toward the goal, where Kreider tapped it past Mason. It was Kreider's first goal since Jan. 21, a span of nine games.
Brassard scored on a power play at 11:42. He took a pass from Brad Richards against a backpedaling Flyers defense and fired a slap shot from just above the left circle through Mason's legs. The goal extended Brassard's point streak to eight games (five goals, five assists).
"We had a decent start in the sense that we forced them to take a couple penalties," Rangers coach Alain Vigneault said. "The power play could have given us the lead there, but their goaltender made some big saves. They made us pay on a couple of opportunities after that, but we battled back hard, won the second period, and in the third period we just didn't get enough looks.
"I didn't mind parts of our game; 5-on-5 I thought we were all right. It was a hard-fought game and they were able to capitalize on a few more of their chances than we were."
Luke Schenn made it 4-2 with 3:45 left in the game. Claude Giroux battled for the puck on a cycle and passed to Scott Hartnell, whose shot was kicked out by Lundqvist right to Schenn, who pushed it into an empty side.
New York had not lost a road game since Jan. 3 at the Pittsburgh Penguins.
"They tightened up a bit in the third," Callahan said. "We were having success in the second getting pucks behind the [defense] and creating things off the cycle and bringing pucks to the net. For whatever reason, whether it was them or us, we didn't generate enough of that in the third period."
Rangers defenseman Dan Girardi, who agreed to a six-year contract extension Friday, was minus-1 in 24:40 of ice time. Callahan, the subject of speculation with the NHL Trade Deadline on Wednesday, had five shots in 20:58.
New York hosts the Boston Bruins on Sunday night.
Philadelphia is 4-0-1 this season in the game after losing by four or more. The Flyers visit the Washington Capitals on Sunday afternoon. Washington defeated Boston 4-2 Saturday and trails Philadelphia by one point in the standings.
The Pittsburgh Penguins lead the division.