TAMPA, Fla. — With 17 seconds to play in regulation in a scoreless duel between the Rangers and Lightning on Monday night, Antti Raanta knew he had to make at least one more save.

Dangerous winger Nikita Kucherov, with five goals and four assists in his previous four games, had the puck on his stick and fired. “He got the rebound there and I just got a little bit lucky. It hit the glove and just went over,” Raanta said. “When I didn’t hear anything, I was sure it went in, but it stayed out.”

As it turned out, Raanta had to make only one more stop in overtime before Ryan McDonagh picked up Victor Hedman’s turnover and fed Mika Zibanejad for a breakaway. His low forehander beat Andrei Vasilevesky (32 saves) on the glove side with 1:04 left in OT for a 1-0 victory.

It was Zibanejad’s second game-winner in six games. “It’s one of the few moves I have,” he said, describing his ninth goal in a season derailed by injury. “So instead of lots of options, I was able to go to that.”

It was the fourth time in the last eight games that the Rangers have battled past regulation. They are 5-0 when playing three-on-three.

“He [Raanta] comes in and he’s right in rhythm,” said McDonagh, who said he took a second to settle the puck before sailing it to Zibanejad for the winner. “Rants was definitely our best player tonight.”

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Raanta, who made 38 saves and posted his third shutout of the season, led the way as the Rangers started their three-game road trip with a determined, feisty effort in their 23rd road win.

“The last couple games, we haven’t been doing the stuff we should be doing when you’re a playoff team,” said Raanta, who is 13-5. “We had a meeting this afternoon and Tanner’s [Glass] fight got us going a little bit. We just needed to be physical and need to have the kind of mentality that we’re not going to be pushed around.”

Starting with perhaps their most contentious period of the season, the Rangers — perhaps emboldened by the presence of Glass — matched the Lightning toe to toe, finishing checks and shoving back. They were credited with 15 hits.

Raanta, who made 35 saves when he last played in the Rangers’ 4-3 overtime victory over the Devils in Newark on Feb. 25, stoned the Lightning for 40 minutes, turning away 25 shots to keep the game scoreless. He also had allowed only one goal on 32 shots against Tampa Bay on Oct. 30 at the Garden.

Early in the third period, Tampa Bay went on its sixth power play when Adam Erne stepped on Brandon Pirri’s stick. Raanta continued to shine against the league’s third-best club with the man-advantage. With 11:08 remaining, Raanta stopped Gabriel Dumont’s backhander at the edge of a scrum and fooled the Lightning forward, who raised his arms in a premature celebration.

The Rangers set the tone early. Brendan Smith broke up a shorthanded two-on-one by intercepting a pass. After 20 minutes, the Blueshirts had 12 shots and Raanta had nine saves, including two with his right pad, first on a screen, then on Ondrej Palat on the doorstep.

Gabriel Dumont jammed defenseman Steven Kampfer’s head into the corner boards, which somehow didn’t draw a major penalty, just a two-minute minor at 14:12. Kampfer eventually rose and went for concussion testing before returning.

A penalty-filled second period followed, and the crowd at Amalie Arena could sense that one goal might be the difference.