Mika Zibanejad scored two goals for a second straight game, and scored in the four-round shootout for New York. Henrik Lundqvist made 39 saves for the Rangers (16-12-4), who have a point in seven of past eight road games (5-1-2).
"This one stings," Zibanejad said.
Zibanejad gave the Rangers a 3-2 lead with his second goal at 1:14 of the third period. Tony DeAngelo passed the puck ahead to Zibanejad entering the Anaheim zone on the left side. He skated in close on Gibson before getting it between his pads.
Zibanejad scored 10 seconds into the game, stealing a pass from defenseman Josh Manson to give the Rangers a 1-0 lead.
Artemi Panarin scored at 3:59 to make it 2-0. Gibson tried to backhand the puck around the boards from behind his net, but Ryan Strome intercepted the pass along the wall and centered a backhand to Panarin.
"You're down 2-0 and I don't think there's four minutes or three minutes gone on the clock yet," Ducks coach Dallas Eakins said. "[Gibson] dug in, and right when he needed to be big, he was as big as a house, and that really lifted our bench a number of times."