Boedker scored in the second and then assisted on Vermette's third-period winner as the Coyotes won on the road in regulation for the first time this season.
Chipchura opened the scoring in the first and then put the game away into an empty net with 23 seconds left in the third as Phoenix moved into a tie for seventh in the Western Conference.
The Canucks were coming off a 2-1-1 road trip but have now dropped three straight at home. They have also now lost two in a row after earning at least a point in 10 of the previous 11 games.
The Coyotes had a pair of quality chances while on the game's first power play in the opening period. David Rundblad threw it to Vermette down low, but his quick redirection went off the post. Boedker then one-timed a cross-ice pass but was robbed by Schneider's glove as he slid across to make the save.
Smith's best stop of the first came when he kicked out his right pad to stop David Booth's backhand in close with about seven minutes remaining.
Chipchura finally opened the scoring at 14:22 with his second goal in his past three games. While battling behind the net, Paul Bissonnette squirted the puck free to Chipchura, who knifed through a passive Canucks defence before cutting in front and roofing a backhand past Schneider.
The Coyotes doubled their lead at 9:54 of the second when Runblad's point shot ricocheted off Maxim Lapierre right to Boedker, who avoided the Vancouver forward's check before beating Schneider under the glove for his fourth of the year.
That goal seemed to wake up the Canucks, who got on the board just 91 seconds later. Ryan Kesler dug the puck out of the boards and threw it to Garrison at the point, who faked a slapshot before ripping a wrist shot past Smith for his third of the year.
Schneider then did his part to keep Vancouver close, robbing Raffi Torres on the doorstep twice just a minute into the third.
But the Coyotes made it 3-1 at 12:32 when Boedker stripped Alex Edler of the puck to create the odd-man rush and then centred for Vermette, who squeaked his fifth of the season through Schneider's pads.
That would be as close as the Canucks would get as Chipchura iced the game with his second of the night and fourth of the season with 23 seconds left.
NOTES: Chipchura now has 51 points in 235 games NHL games. ... Bissonnette has assists in three consecutive games after going pointless through eight contests. It is the first point streak of his five-year career. ... Phoenix was missing Martin Hanzal and Radim Vrbata, out with injuries for their third and fourth straight games, respectively. Vrbata is the team's leading scorer and Hanzal has a team-high seven goals. The Coyotes were also without the services of defencemen Derek Morris and David Schlemko. ... Vancouver was without defenceman Kevin Bieksa, missing his second straight game with a sore groin. ... Henrik Sedin played in his 600th consecutive game. Only Calgary defenceman Jay Bouwmeester has a longer ironman streak currently going (606 games).