It was Quickâ€s first shutout of the season and the 64th of his career, moving him into a tie with Henrik Lundqvist for 17th most in NHL history.
Mika Zibanejad scored for the Rangers (4-5-2) late in the first period off a give-and-go with Will Cuylle, and Sam Carrick added an empty-net goal with 95 seconds left on the game clock.
The Canucks (5-6-0) got 23 saves from Thatcher Demko, but struggled to generate offence and were outshot 25-23.
Rangers captain J.T. Miller played his first game back in Vancouver since being dealt to New York by the Canucks at the end of January.
Both benches joined the crowd at Rogers Arena in a standing ovation after Miller’s tribute video was shown on the big screen midway through the first period.
Canucks: Winger Conor Garland did not return for the third period after getting levelled by Carrick at the end of the first period. Vancouver was already missing several players due to injury, including captain Quinn Hughes. The star defenceman missed a second straight game with what head coach Adam Foote described as a lower-body injury. Foote said earlier Tuesday that Hughes is “day to day” and will be re-evaluated on Wednesday.
Rangers: The result snapped a three-game losing skid for New York, which came in with just one win over its last seven games (1-4-2). The Rangers were outscored 22-12 across those seven games.
Quick made a flurry of saves just over six minutes into the third period, including denying Elias Pettersson from the top of the crease to keep Vancouver off the scoreboard.
The Rangers have yet to win at home this season but are now 4-1-1 on the road.
Rangers: Visit the Edmonton Oilers on Thursday.
Canucks: Kick off a three-game road trip against the St. Louis Blues on Thursday.
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