Philippe Dupuis had a short-handed goal and two assists. Milan Hejduk and Brandon Yip also scored for the Avalanche. Matt Duchene chipped in with two assists.
Dallas came into the game leading the league in goals per game (3.58) and had scored six goals in Phoenix on Friday night, but Budaj kept the high-scoring Stars off the board. He made 14 saves in the second period and benefited from two hit posts en route to his first shutout since Dec. 7, 2009.
Meanwhile, his team was peppering Andrew Raycroft with a season-high 45 shots.
Colorado got on the board midway through the first period.
Porter, who was recalled from Lake Erie of the AHL on Friday, put the Avalanche ahead 1-0 with his first goal of the season. David Van Der Gulik set it up by outworking Dallas defensemen Nicklas Grossman and Stephane Robidas to feed Porter in front of the net. Porter put a backhand by Raycroft with 9:58 left in the first period.
Hejduk made it 2-0 with his fifth goal of the season when he lifted a backhand over a sprawled Raycroft at 4:53 of the second period. The Avalanche extended the lead to 3-0 later in the period.
With Colby Cohen in the penalty box for roughing, Dupuis picked up a loose puck near center ice, skated into the Dallas end and beat Raycroft with a slapshot over his left shoulder with 6:56 left in the second.
The Avalanche blew it open with two goals in a 31-second span early in the third. Dupuis stole a puck from Dallas defenseman Jeff Woywitka and fed Porter, who scored to make it 4-0. Right after that Yip redirected Duchene's centering pass by Raycroft to finish the scoring.
Notes: Budaj's victory gives him 90 career wins with the Avalanche, third in franchise history behind Patrick Roy (262) and Dan Bouchard (107). ... Dupuis' goal was the first of his career. ... Avalanche G Craig Anderson (right knee injury) is working out and could return in a week or two.