Anaheim (20-12-1) improved to 2-2-0 through the first four games of a five-game road trip that will conclude at the Columbus Blue Jackets on Tuesday. New York (16-14-4), meanwhile, has dropped four of its past five (1-2-2).
"I think we played a pretty good game 5-on-5, it basically came down to special teams," Rangers captain J.T. Miller said. "The penalty kill was really good today, just gave up one there at the end. The power play wasn't sharp enough, and we gave one up, so that's the game."
Matthew Robertson scored, and Igor Shesterkin made 22 saves for the Rangers, who had their four-game home point streak end (2-0-2). They fell to 4-9-3 at home and were held to one goal or fewer for the ninth time in those 16 home games.
New York played without center Mika Zibanejad, who was a healthy scratch because he missed a team meeting Monday morning, coach Mike Sullivan said.
"I'm not going to get into specifics on why we made decisions the way we made them," Sullivan said. "We believe strongly in a process that we've put in place here for our team, and it's as simple as that. We have a certain set of expectations that we all hold ourselves accountable to. At the end of the day, that's what it's about, and we all take ownership and responsibility for it. Mika and I had a discussion, we made a decision, and we move on. He's an important player for us. He's a terrific player and he's a terrific person."
Gauthier gave Anaheim a 2-1 lead at 5:51 of the third period, scoring at the end of a Ducks power play. Beckett Sennecke snuck past Miller to carry the puck into the offensive zone on the right side. He sent a pass across to Gauthier, who scored from above the left hash marks with a shot past Shesterkin's blocker.
"The pass (to me) was a little in front and I kind of just poked it ahead," Sennecke said. "I just kind of looked up and saw Cutter, passed it to him on his tape and he did the rest. I said it to him, (but) there's not many people in the world that can shoot a puck like he can. It's pretty incredible to watch. It's on and off his stick in a heartbeat. It's like rising. It's a bullet."
Gauthier said he worked on his shot during the morning skate with Julien Tremblay, who is the Ducks' NHL player development coach.
"I wanted to work on getting shots through defensemen," he said. "I feel like a lot of this season I've been getting shots off the rush and I'm either whiffing them or hitting defensemen in the legs. The biggest thing is to get it on and off quick and try to be as accurate as you can. Beckett made a really nice pass to me and I just tried to shoot it."
Gauthier scored an empty-net goal to make it 3-1 at 19:38 before Pavel Mintyukov scored with Shesterkin in the net at 19:57 for the 4-1 final.
"I thought for two periods we really liked our game," Sullivan said. "In the third period, when they scored right at the very end of their power play, we didn't seem to have the push that we hoped for down the stretch to get that goal back."
LaCombe scored his short-handed goal at 7:18 of the second period to give the Ducks a 1-0 lead. It came six seconds after the Rangers had a 5-on-3 advantage, and 17 seconds after Dostal came across to stop Vincent Trocheck's shot from the left side into what looked like an open net.
