Josh Brown put the Coyotes ahead 1-0 at 5:46 of the second period, scoring from the right circle after Guenther's initial shot produced a big rebound.
J.T. Miller tied it 1-1 at 18:32. Tyler Myers' slap shot from the top of the left circle hit Miller's skate in front as he was battling for position before he slid the puck in with his backhand.
Miller has 12 points (three goals, nine assists) during a nine-game point streak.
Kolyachonok, a defenseman who was recalled earlier in the day from Tucson of the American Hockey League, put the Coyotes ahead 2-1 at 19:28 with a shot from the right point that hit Canucks forward Dakota Joshua and deflected five-hole on a screened Silovs.
Guenther made it 3-1 at 1:55 of the third period with a one-timer from the edge of the crease after Cooley stole the puck from Hughes below the goal line.
“Their [defensemen] are really good back there and they can make a lot of plays, so we want to limit their time and space as much as possible, and I thought we did that,” Cooley said. “I was fortunate to pickpocket that and found Guenther, and when he's open in the slot like that, it's going in.”
Guenther was not made available to the media after the game but Arizona coach Andre Tourigny had plenty of praise for the forward.
“He played the game the right way," Tourigny said. "He wants to play the right away, he has great value, he will be a great leader. He's a blessing for us.”