The Avalanche were on the power play when Stastny netted his first goal at 11:50 of the first period. Brandon Yip came around from behind the net and fired a shot that goalie Andrew Raycroft blocked but couldn't control. The rebound came back out to Yip, who pushed the puck back toward the net. There was another rebound that Stastny got to and knocked past Raycroft.
It was the first goal of the preseason for Stastny, who had 20 goals and 79 points last season.
Stastny scored again at 16:51 of the second.
James Neal cut Dallas' deficit to 2-1 with 4:35 remaining.
Budaj, the backup to Craig Anderson, was solid throughout. He turned away several solid scoring opportunities that the Stars produced in the first period.
The Stars finally broke through with James' late power-play goal. Dallas had another power play in the closing minutes and pulled Raycroft with about 90 seconds remaining for an extra attacker. Budaj stopped Dallas' best opportunity in the final moments with a stick save of Adam Burish's slap shot from the point.
The Avalanche (2-3) and the Stars (2-2) will meet in another exhibition game Thursday in Dallas.
Copyright by STATS LLC and The Associated Press
Arena: Pepsi Center Location: Denver, Colorado
Referees: Kelly Sutherland, Steve Kozari Linesmen: Darren Gibbs, Shane Heyer
Paul Stastny 1 (power play) Assist: Brandon Yip, Matt Duchene
Paul Stastny 2 Assist: Adam Foote, Brandon Yip
James Neal 2 (power play) Assist: Severin Blindenbacher, Loui Eriksson