Trocheck gave the Rangers a 1-0 lead with a power-play goal at 3:38 of the first period.
The Canucks scored the next three goals, the first coming 53 seconds later when J.T. Miller scored with a one-timer from the left face-off circle off a pass from Pettersson to make it 1-1 at 4:31.
Hoglander's one-timer from the slot got past Shesterkin at 6:45 to give Vancouver a 2-1 lead. The play started with a quick-up pass through the neutral zone from Hughes to Sam Lafferty.
Hughes did it again to help set up Boeser's goal that made it 3-1 at 19:44.
Boeser scored off the rush after Hughes hit Pettersson with a bank pass up off the right-wing wall while the Rangers were changing their defense pair. Pettersson moved the puck up to Boeser past K'Andre Miller, who had just come on the ice. Boeser deked to his backhand and roofed his shot past Shesterkin.
"We made mental mistakes," Rangers coach Peter Laviolette said. "We made line change mistakes, we made turnover mistakes. I don't feel like we were in our end taking heat the entire night, but the mistakes that we made they were loud, I mean they were really loud. It's just too much for our goaltenders. We've got to be better than that."
Panarin scored from the right circle at 8:19 of the second period to cut it to 3-2.
But Pettersson made it 4-2 at 15:33, scoring off his own rebound by getting the puck back, going to his backhand to get it around Shesterkin's left pad and then to his forehand to tuck it in.
Hoglander pulled the puck bwteeen his legs to his backhand and scored at 16:47 to extend the lead to 5-2.
"I've seen that before," Pettersson said of Hoglander's move on his goal. "He plays like that, which he should. He plays with a lot of speed. It's a countryman right there scoring a nice goal. I was excited for him."
Trocheck scored from the left circle to make it 5-3 at 3:36 of the third period. Pettersson scored into the empty net at 18:29 for the 6-3 final.
NOTES: Hughes' defense partner, Filip Hronek, was also plus-4 with two assists. ... In the two games they've played together on the same line, Miller, Boeser and Pettersson have combined for 16 points (eight goals, eight assists). … Pettersson has scored twice in two straight games and three of four. … Hoglander hadn't scored two goals in a game since Dec. 10, 2021. … Trocheck has three straight multipoint games and four in five games. He has 11 points (four goals, seven assists) in his past five games.