Marek Svatos also scored, David Jones added an empty-netter, and Paul Stastny had three assists. The Avalanche snapped a two-game skid to remain on top of the Western Conference standings and tie Pittsburgh for the overall lead.
Colorado also improved to 5-0 at the Pepsi Center, one win away from tying its best home start since moving to the Mile High City.
Budaj was brilliant in goal, allowing only Ed Jovanovski's power-play goal midway through the third period.
Trailing 2-1 with just over a minute remaining, the Coyotes pulled goalie Ilya Bryzgalov, leading to Jones' breakaway goal.
Just 19 seconds later, Hejduk scored his second of the night.
The 27-year-old Budaj was scheduled to make his first start Oct. 23 against Carolina, but was scratched due to flu-like symptoms. It turned out to be swine flu, causing Budaj to miss four games.
With Budaj back and healthy, Craig Anderson finally got a night off. Anderson made a franchise-record 15 straight starts to begin the season, breaking the mark that belonged to Mario Gosselin, who made nine straight starts to open the 1987-88 season.
Bryzgalov made 25 saves as the Coyotes dropped their second straight game. Bryzgalov has one of the top goals-against averages in the NHL, allowing less than two goals a game.
The Avalanche scored a power-play goal just 57 seconds into the game when Hejduk tipped in Kyle Quincey's slap shot from the blue line.
In the third period, Svatos jammed in a loose puck rolling close to Phoenix's goal.
Cody McLeod returned to the ice Wednesday after missing six games following an inadvertent stick to his left eye.
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