Arthur Kaliyev of the Rangers celebrates his second-period goal against...

Arthur Kaliyev of the Rangers celebrates his second-period goal against the Ottawa Senators with his teammates at Madison Square Garden on Tuesday. Credit: Jim McIsaac

Every game is big now for the Rangers, who continue to pull themselves out of the death dive they were in for all of December and are now trying to battle their way back into the playoff picture.

A game Tuesday at Madison Square Garden against Ottawa, which held the first wild card spot in the Eastern Conference, was another big one for them. And it couldn’t have gone any better.

Five different Blueshirts, including Matt Rempe, scored, and goalie Igor Shesterkin made 20 saves in posting his second straight shutout as the Rangers blew out the visiting Senators, 5-0, to not only extend their point streak to nine games (6-0-3), but to also pull themselves within two points of a playoff spot.

“I thought this was the best, most complete game since I’ve been here,’’ said Arthur Kaliyev, who scored his second goal since the Rangers claimed him off waivers from L.A. on Jan. 6. “We didn’t give much. We clogged up the neutral zone against them, played really good in the ‘D’ zone, covering their top players and everything. And that turned into great offense for us, too.’’

And the Rangers (23-20-4, 50 points), also showed toughness and togetherness, fighting back after Ottawa captain Brady Tkachuk knocked over Shesterkin when the goalie tried to cover a loose puck near the goalpost early in the third with the Rangers leading, 3-0. The Blueshirts swarmed Tkachuk while Shesterkin lay on his back for a moment before rolling over onto all fours. Then Shesterkin got up and went into the pile after Tkachuk.

“I just got a couple punches from Tkachuk,’’ Shesterkin said. “To be honest, his hit on me, I did not really enjoy that, because I was between the pipe and him ... I didn’t want to jump [into the scrum] there, but I saw he was the third man on a fight between our guy and their guy. So I just tried to hold him. But he wanted to fight. And it’s tough for me, because I cannot drop my gloves. If I do that, I go to locker room [with a game misconduct].’’

Shesterkin got a penalty for leaving the crease, while Tkachuk and Rempe got double roughing minors, and Shane Pinto got a roughing minor. After all was said and done, the Rangers ended up with a power play, and when Michael Amadio then ran into Shesterkin behind the net as he tried to play a puck, the Rangers got a 5-on-3 power play. They scored on both ends, with Artemi Panarin (at 9:01) and then Will Cuylle (at 9:57) pushing the score to 5-0.

And it could have been more. Two other apparent goals, one by Sam Carrick and a second by Kaliyev, were overturned on video review in the first two periods after coaching challenges. And another that was batted in by Cuylle early in the third period was waved off because it was hit with a high stick.

Carrick’s shot from the right wing banked in off the far goalpost with 2:28 left in the first period, but Ottawa coach Travis Green challenged the play that the Rangers had entered the zone offside. Video review determined that Rempe had indeed crossed the blue line before the puck did on the entry, so the goal came off the board.

But just 1:16 later, Alexis Lafreniere backhanded in the rebound of Adam Fox’s shot that had been tipped on goal by Vincent Trocheck and the Rangers were up, 1-0. The goal, Lafreniere’s 13th of the season, was his second in two games, after having scored in his hometown of Montreal on Sunday.

Kaliyev made it 2-0 at 1:50 of the second period when he corralled the puck after Urho Vaakanainen’s shot was partially blocked and, while leaning back, whipped a shot off the shoulder of goalie Leevi Merilainen and in.

“I was like, I might as well,’’ Kaliyev said of the shot. “I’ve had those go in before, and I thought it had a chance of going in if it’s in the ‘O’ zone.’’

Kaliyev appeared to score his second goal at 5:31 when he cut to the middle of the slot and fired one past Merilainen, but Ottawa again challenged the goal for offsides and on video, the officials determined Filip Chytil had crossed the blue line before the puck, nullifying the goal.

After that challenge, Green pulled Merilainen — who officially had made 14 saves on 16 shots in 24:59 — in favor of Anton Forsberg.

Rempe’s goal, a pretty backhander off a feed from Adam Edstrom at 3:34 of the third period, made it 3-0.

Notes & quotes: Thirteen Rangers had at least one point with Lafreniere (one goal, one assist) and Fox (two assists) getting two each ... Defenseman K’Andre Miller (25) and backup goaltender Jonathan Quick (39) celebrated their birthdays.

SUBSCRIBE

Unlimited Digital AccessOnly 25¢for 6 months

ACT NOWSALE ENDS SOON | CANCEL ANYTIME