Keith Yandle had a goal and an assist, Scott Upshall and Kyle Turris also scored and Lee Stempniak had two assists to help the Coyotes run their road winning streak to five games.
Matt Duchene and Ryan Stoa scored for Colorado and Craig Anderson made 25 saves in relief of Peter Budaj.
Yandle, Phoenix's lone representative in the All-Star game Sunday in Raleigh, N.C., made it 2-1 with his eighth goal of the season and chased Budaj with 6:01 left in the first period. Yandle took a drop pass from Martin Hanzal and beat Budaj with a shot to the top left corner.
Budaj made eight saves before being benched.
The Coyotes made it 3-1 1:09 into the second period when Belanger stuffed the puck into the corner.
Colorado, which had just one shot in the first period and seven through the first 30 minutes, gained momentum late in the second period. The Avalanche started pressuring Bryzgalov, finishing with 16 shots in the period. They had a goal waived off when Cody McCloud fell into Bryzgalov as Phoenix defenseman Sami Lepisto knocked the goal off its moorings.
Colorado continued to apply pressure in the third, but Turris scored with 7:06 left to ice the game.
Duchene scored his 20th goal of the season with 4:16 left before Belanger scored an empty-netter with less than a minute remaining
The Avalanche took a 1-0 lead early in the first on Stoa's second goal in two games. The Coyotes tied it 7 seconds into Paul Stastny's interference minor on Upshall's team-leading 15th goal of the season.
NOTES: Peter Forsberg worked out with the Avalanche during the morning's skate, the fifth straight day the former Hart Trophy winner has practiced with the team as he contemplates a comeback after a three-year layoff from the NHL. ... Yandle extended his points streak to nine games. ... Colorado RW David Jones injured a shoulder in the second period and didn't return.