Dakota Joshua, Drew O'Connor and Brock Boeser scored, and Kevin Lankinen made seven saves on 11 shots for the Canucks (32-26-12), who have lost three of four (1-2-1) and fell three points behind the St. Louis Blues for the second wild card in the Western Conference. The Blues won 4-1 against the Chicago Blackhawks on Saturday.
Vancouver is also one point behind the Calgary Flames after the latter's 4-3 overtime victory at the New York Islanders.
The Canucks played the third period without forwards Elias Pettersson and Nils Hoglander, who didn't return to the game because of undisclosed injuries. Coach Rick Tocchet said it's doubtful either will be able to play at the New Jersey Devils on Monday, the third of a six-game road trip. He said they would likely have to recall a center from Abbotsford of the American Hockey League.
Vancouver was already playing without center Filip Chytil, who is out with an upper-body injury and is not on the road trip.
"Can't really complain too much with how we played," Canucks captain Quinn Hughes said. "I thought we competed hard, especially with two forwards down, going to 10 forwards in the third period.
“We're playing gutsy now. … Nine times out of 10 I think we walk away with that one, but in this instance we don't."
Joshua gave Vancouver a 1-0 lead at 11:51 of the first period, scoring off his own rebound of a shot that hit the left post.
The Canucks outshot the Rangers 11-1 in the first.
"You can't start the game like that, start a period like that," New York coach Peter Laviolette said. "They were just quicker than us. They had the puck on their stick, and we were just chasing them."