Chipchura netted the first and last goals of the game, giving the visitors a lead in the opening period before closing the door on Vancouver in the final seconds of the third.
The Coyotes had recently blown leads in close losses to Edmonton and Calgary but were able to hold on against the Canucks.
"We're a team that usually hangs on to leads pretty well and we coughed up two on this trip," Chipchura said. "We looked at it like we could get three points out of this (three-game road) swing and make it a decent trip."
Mikkel Boedker scored in the second, and Antoine Vermette in the third to provide a 3-1 advantage for the Coyotes (9-7-3), who held firm behind Mike Smith's 29 saves.
The Canucks (10-5-4), who lead the Northwest Division, dropped a third consecutive home game and were unable to rebound positively from Sunday's 8-3 blow-out at the hands of Detroit.
Vancouver got on the board through Jason Garrison's slap shot, and again pulled within a goal in the third behind Henrik Sedin's score, but they could not find an equalizer.
Cory Schneider made 18 saves in the defeat and left unhappy with his recent performances.
"I'm kind of tired of playing like an average goalie, it's getting ridiculous now," Schneider said. "You got to make some big saves to give your team a chance to at least get a point."