PHILADELPHIA -- Alexis Lafreniere scored, Matt Rempe netted his first career goal and sparked his streaking club with a first-period fight, as the New York Rangers tied a franchise record with their 10th straight victory, defeating the Philadelphia Flyers 2-1 on Saturday.

Igor Shesterkin made 39 saves for the surging Rangers, who can set a club mark for consecutive victories on Sunday at Columbus. The Rangers, who are leading the Metropolitan Division, have not lost since Jan. 26.

"It was good," Rangers coach Peter Laviolette said of the win. "It had a little bit of everything."

Rempe, promoted from the American Hockey League last week, is the first Rangers skater with a goal and a fighting major in the same game within the first five games of their career since Ryan Callahan in March 2017, according to ESPN Stats & Information research. Philadelphia veteran Nicolas Deslauriers battled Rempe in a heavyweight duel just three minutes into the game. Both players landed heavy punches, with Deslaurier getting cut on the forehead by one of Rempe's hard right hands. The fight ended with Deslaurier tackling Rempe to the ice.

"That's a good, old-fashioned hockey fight," Philadelphia coach John Tortorella said.

But Rempe's goal proved much more valuable, as he scored the game winner at the 6:31 mark of the third period, helping New York tie its franchise season record of consecutive wins, matching runs from the 1939-40 and 1972-73 seasons. It's also the NHL's longest winning streak this season behind the Edmonton Oilers' 16-game surge from Dec. 21 to Jan. 27.

Rempe, a 6-foot-7 rookie sixth-round pick playing in his fourth career game, deflected Barclay Goodrow's shot off his right skate and past goaltender Samuel Ersson with 13:29 to play. Ersson made 22 saves in the loss.

"That's unreal. It's probably the ugliest first goal in NHL history, but I'll take it," Rempe told ESPN after the win. "It's unreal, I'm having a blast."

His coach disagreed on Rempe's description of the tally.

"He did exactly what he's supposed to do, which is go to the front of the net and stand in front of the goaltender," Laviolette said.

Tyson Foerster scored for Philadelphia, which was defeated for just the third time in its last eight games. The Flyers, in third place in the Metropolitan Division, are now 15 points behind New York.

Lafreniere gave the Rangers a 1-0 lead with 8:04 left in the second when his wrist shot got through Ersson during a 4-on-4 situation. It was his 17th of the season and third in two games.

The goal capped a wild sequence that began when Philadelphia's Garnet Hathaway was whistled for a double-minor high-sticking penalty. Philadelphia, which entered leading the NHL with 13 short-handed goals and the league's second-best penalty-killing unit, nearly got on the board, but Scott Laughton's wrist shot that beat Shesterkin went off the crossbar.

Lafreniere almost scored on the power play two minutes after Laughton's miss, but Ersson made the save of the game, denying the backhand try with a stellar left pad save. Philadelphia then nearly had another great short-handed chance, but Artemi Panarin held Cam Atkinson, resulting in a Rangers penalty and a 4-on-4 situation.

Philadelphia tied it 2:36 into the third when Foerster finished in front after a nifty pass from behind the net from Laughton.

Rempe and Deslauriers jawed in the pregame warmups and it carried over to the ice, adding to the rookie's memorable month. Rempe fought New York Islanders tough guy Matt Martin in his debut on Sunday and was ejected for a hit to the head of New Jersey Devils forward Nathan Bastian in New York's 5-1 victory Thursday.

"He played a heck of a game," Laviolette said after Saturday's win. "Had a great fight. Had big hits. Put the puck behind the defense. He's been great since he's been here. You can tell the players in the locker room love having him here. He loves to hit and be physical."

Rempe entered with 22 penalty minutes in just 9:47 of ice time in three career games. The 33-year-old veteran Deslauriers is no stranger to the penalty box, having served 729 penalty minutes in 635 games entering Saturday.

The scrap seemed to ignite both teams for the afternoon start.

Philadelphia's leading scorer, Travis Konecny, did not play due to an upper-body injury. He has 27 goals and 54 points this season.

The Associated Press contributed to this report.