"No matter how well a team is playing, you should still be able to get stuff to the net," Canucks coach Willie Desjardins said. "We had some chances in the first three minutes that didn't hit the net and we didn't have much after that."
Vancouver got its first shot 8:12 into the second period when Alexandre Burrows put a long shorthanded shot on Smith from inside the Canucks blue line.
After Ryan White deflected Oliver Ekman-Larsson's shot behind the Vancouver net, Crouse scored on a wraparound at 12:56. His third goal of the season was his first in 19 games.
"I used everything I had, I think I even dove a little bit to get there," Crouse said.
Arizona made it 2-0 after Sven Baertschi got a double-minor penalty for high-sticking Christian Dvorak. Burmistrov beat Miller with a wrist shot at 4:29 of the third period.
It was Burmistrov's sixth point in six games since Arizona claimed him on waivers from the Winnipeg Jets. It was his first goal in 42 games, since March 16, 2016, when he scored for Winnipeg against Vancouver.
"If you don't score on that power play, that gives them some life and a lot of energy," Arizona coach Dave Tippett said. "That was a big goal."