Brandon McMillan, Shane Doan and David Moss also scored for the Coyotes, who improved to 4-0-2 in exhibition play. Oliver Ekman-Larsson added two assists.
Derek Dorsett and Radim Vrbata replied for Vancouver (3-2-0), which got 31 saves from Ryan Miller.
Tied 1-1 after the first period, the Coyotes struck twice in the second to put the game out of reach. MacMillan made it 2-1 at 10:55 when his shot was stopped by Miller and rebounded in off Vancouver defenceman Luca Sbisa.
Doan then stretched the lead to two on the power play with 1:15 left, deflecting home Mikkel Boedker's shot from the point.
A lot was made before the game about Canucks head coach Willie Desjardins putting former first-round picks Bo Horvat, Hunter Shinkaruk and Nicklas Jensen together on a line. The trio made their first real impact with the score still tied 1-1 early in the second, buzzing around the Coyotes zone but failing to find the mark.
Daniel Sedin then had a great chance off a feed from brother Henrik that Smith handled, before Alexandre Burrows ripped another shot wide of the Arizona goal from the slot.
Vancouver's only other real chance of the period came while trailing 2-1 when defenceman Alexander Edler found himself down low, but chose to try a pass that was blocked instead of directing a shot at Smith.
Arizona's Martin Erat almost made it 4-1 four minutes into the third period, ripping a shot off the post that stayed out behind Miller.
Horvat, Shinkaruk and Jensen then had an energetic shift but again couldn't get anything past Smith before heading off to a big cheer from the crowd at Rogers Arena.
Vrbata, who signed with Vancouver as a free agent in July after five years with the Coyotes, made it 3-2 on Vancouver's first power play of the night on a shot that somehow found its way through Smith with exactly nine minutes to go in regulation.
But that would be as close as the Canucks would get as Moss sealed it off a big rebound in front of Miller with 1:41 remaining.
Both teams dressed lineups similar to the ones they will go with once the regular season gets going. Missing out for the Canucks were defencemen Dan Hamhuis and Kevin Bieksa, and forwards Zack Kassian, Brad Richardson and Jannick Hansen. Notable absences for the Coytes included forwards Sam Gagner and Lauri Korpikoski.
Vancouver opened the scoring at 4:43 of the first period when Chris Higgins one-timed a shot from the faceoff dot off the rush that Smith only got a piece of. The puck dribbled towards the goal-line and the hard-charging Dorsett poked it home.
Arizona tied things at 12:02 on a play Miller might want to have back. The Coyotes flipped the puck out of their zone and the Vancouver goalie decided to stay in his net instead of going out to play it, allowing Vitale to move in and beat him through the pads.
It was the first goal allowed by Miller — who also signed as free-agent this summer — in pre-season after he faced a mere seven shots against in just over 30 minutes of action against the Calgary Flames on Friday.
Notes: Canucks defenceman Frank Corrado suffered an upper-body injury in the second and did not return. ... The Canucks play their next pre-season game in Edmonton on Thursday before wrapping up the exhibition schedule on Saturday at home, again against the Oilers. ... Arizona visits Edmonton on Wednesday before hosting the San Jose Sharks on Friday. ... The Canucks open the regular season Oct. 8 on the road against the Calgary Flames. The Coyotes will kick things off Oct. 9 at home against the Winnipeg Jets.