Mason McTavish and Troy Terry also scored for the Ducks, who had dropped six of their last seven coming into the game. At 20 games, Anaheim just missed tying the Arizona Coyotes for most games to start the season without picking up a regulation victory.
Barclay Goodrow and Braden Schneider scored for New York, and Jaroslav Halak stopped 19 shots.
Artemi Panarin picked up his 400th career assist on Schneider’s goal. Penarin had a chance to tie it with 3:46 remaining, but his shot hit the post and Kaapo Kakko missed tipping it in.
Gibson made his share of great saves to keep the Ducks in the game, including stopping Kakko on the breakaway midway through the second period.
Goodrow blocked John Klingberg’s shot in the Ducks’ offensive zone, rushed up ice and then put a wrist shot through Gibson’s pads to open the scoring at 8:51. It was Goodrow’s 50th career goal and fifth of the season.
The Ducks answered 31 seconds later when McTavish knocked in a rebound after Halak made a pad save on a shot from the point by Kulikov. It was McTavish’s third of the season with all of them coming in the last nine games.
Kulikov put Anaheim up 2-1 just 39 seconds into the second with a wrist shot from the side boards that trickled between Halak’s pads and into the net.
Terry made it a two-goal advantage five minutes later with a snap shot from just inside the left faceoff circle that went top shelf inside the far post. It was Terry’s eighth goal of the season and his third in the last six games.
Schneider scored for the second straight night and got the Rangers within 3-2 with a wrist shot through traffic.