Rangers right wing Julien Gauthier is congratulated after scoring against the Sharks...

Rangers right wing Julien Gauthier is congratulated after scoring against the Sharks during the third period of an NHL game in San Jose, Calif., on Saturday. Credit: AP/Jeff Chiu

SAN JOSE, Calif. – The Rangers could afford to be all smiles late Saturday night, after finally pulling out a late 2-1 victory over the San Jose Sharks. The smiles were expressions of relief, more than anything.

They really needed this one.

“Sure did,’’ coach Gerard Gallant said. “You know, when it's 0-0, and as well as we played, and you could just feel like they were going to get one of those deflection goals. That's what you felt like on the bench, you know? And I'm sure when that went in, it was a big relief for us.’’

Since a 1-0 overtime victory over the Philadelphia Flyers on Nov. 1, the Rangers had been 2-3-2, and had a habit of losing games in which they felt they’d played well, but just couldn’t score the decisive goal when they needed to.

Despite dominating for most of the game Saturday, and ultimately outshooting coach David Quinn’s Sharks, 43-23, the Rangers were locked in a scoreless battle late in the third period. Then fourth-line winger Julien Gauthier managed to tip a shot by Jacob Trouba past goaltender James Reimer to get the Rangers on the board with 6:03 left. Adam Fox followed that with an empty-net goal with 1:07 remaining, and that turned out to be the game-winner after San Jose’s Logan Couture scored for the Sharks with 16.1 seconds left.

The victory lifted the Rangers (9-6-4) to 1-0-1 on their four-game West Coast trip, which concludes with games in Los Angeles vs. the Kings Tuesday and Anaheim vs. the Ducks Wednesday.

Gallant was in a good mood after the win, because he said he believed the team had played its best, most complete game since the 3-1 win over Tampa Bay on Opening Night that he’s so often referenced. They generated many chances, and even when Reimer turned aside their shots, or they saw the puck bounce off the goalpost or crossbar, which it did several times, the Rangers kept coming.

“We were a little frustrated the puck didn't go in the net, trust me,’’ Gallant said. “But they didn't lose their focus. They kept pushing and pushing, because they were playing well, and the chances were there. There were a lot of ‘Grade A’ chances … and Reimer made some great saves. And they also hit three or four posts.’’

The Rangers also got a great game from goaltender Igor Shesterkin, who, despite seeing only 23 shots on goal, was spectacular when he needed to be to keep the 6-11-3 Sharks off the board when it mattered. The performance by Shesterkin, whose play seems to be getting stronger in recent weeks, is what kept the Rangers from getting discouraged when all their shots weren’t going in, according to defenseman K’Andre Miller.

“I give credit a lot to our goalie back there,’’ said Miller, who had the secondary assist on the Gauthier goal. “He's been unreal, obviously. Since I've joined this team, he's been that guy that can win games for us, singlehandedly.

“But I think it was just a matter of playing a full 60 minutes,’’ he said. “I think it was a full team effort, and the full 60 that we were looking for.’’

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