The Rangers' power play responded early in the third period, with Lafreniere extending the lead to 4-2 off a pass from Perreault at 1:04. Perreault was on the first power-play unit to start the third period, replacing Pavel Dorofeyev, who Sullivan said he thought "was fighting it a little bit."
Lafreniere scored with Lankinen out of the crease after contacting Miller above the blue paint. The officials conferred briefly and the goal stood with no coach's challenge from Vancouver.
Perreault made it 5-2 at 5:57, scoring on a deflection of Adam Fox's shot.
Cuylle added one off a rebound at 15:22 for the 6-2 final.
"I didn't think we were as clean in the first half of the game," Sullivan said. "I thought we got better as the game went on. I thought the third period we were terrific."
Said Malhotra: "It's disappointing when you let the game get away from you like that. Lack of details. Lack of intensity to finish the game and the final score ends up being what it is."
Kartye got the Rangers going early, scoring 27 seconds into the game to give them a 1-0 lead.
Vancouver tied it 1-1 on DeBrusk's goal at 17:04 off a sharp-angled shot from the left circle.
Cuylle gave the Rangers a 2-1 lead with a shot past Lankinen's glove from the top of the left circle at 2:09.
Pettersson tied it 2-2 with his first career short-handed goal at 16:56.
"Bad third period," Canucks forward Drew O'Connor said. "I thought our first two periods, we were pretty good and we were right in the game. We give up one early on the PK. We have to do better there. We kind of let it snowball after that."