NEW YORK -- Igor Shesterkin made 20 saves en route to a shutout, and even entered into a fight behind his own net in the third period, as the New York Rangers blanked the Ottawa Senators 5-0 on Tuesday night.

With 12:51 remaining in the game and New York leading 3-0, a scrum ensued in front of Shesterkin's net, centered around Ottawa captain Brady Tkachuk. Shesterkin appeared injured as he knelt in his crease while the scrum gravitated toward the boards. About halfway through the fracas, however, Shesterkin leaped to his skates and charged after Tkachuk before the former Vezina Trophy winner was greeted by a left hand from the fiery Senator.

"I just got a couple punches from Tkachuk," Shesterkin said with a laugh after the win. "To be honest, there was a hit on me [before the whistle], and I didn't really enjoy it. ... So, I just wanted to go over and hold him, and if he wanted to fight, it's tough for me, because I cannot drop my gloves."

Rangers forward Matt Rempe, who is known for fighting and has no problem dropping his gloves, was a part of the mix behind the net, as well.

"I was a little nervous because I don't want anything to happen to him," Rempe said of seeing his goaltender involved in the scrap. "But I love it because he's a competitor, and I just wanted to make sure I get in there and nothing happens to him."

Rangers coach Peter Laviolette enjoyed the moment, as well, telling reporters after the win, "That's hockey, man."

Alexis Lafreniere had a goal and an assist in the New York win, and Arthur Kaliyev, Rempe, Artemi Panarin and Will Cuylle also scored. The Rangers are now 7-1-3 since Jan. 2 and have won three straight at home. The shutout was Shesterkin's third this season and the 18th of his career.

Lafreniere beat Ottawa netminder Leevi Merilainen for his 13th goal at 18:48 of the first. Kaliyev made it 2-0 at 1:50 of the middle period with his second goal as a Ranger since being claimed off waivers from Los Angeles on Jan. 6.

Kaliyev appeared to score again at 4:59 but the goal was waved off for offside. Rangers forward Sam Carrick had a goal negated for the same reason just before Lafreniere's goal.

Anton Forsberg replaced Merilainen in net for Ottawa after the challenge on Kaliyev's play. Merilainen made 14 saves before his departure. Forsberg finished with 10 saves.

Rempe scored his first this season at 3:34 of the third, depositing a backhand past Forsberg. Panarin made it 4-0 with his 20th goal on the power play at 9:01 before Cuylle completed the scoring at 9:57.

The Senators entered the contest on a 5-0-1 stretch in their past six games.

"We've been playing some good hockey," Ottawa coach Travis Green said. "But we weren't good enough to win [tonight]. We fought the puck all night; we weren't good enough with the puck."

The Associated Press contributed to this report.