Stastny picked up his first career hat trick, Wolski added a goal, and Budaj made 31 stops in the Avalanche's 4-3 win over Dallas at the Pepsi Center in the 2007-08 season opener for both teams on Wednesday.
Niklas Hagman -- playing in his 400th NHL game -- had a goal and an assist, and Jeff Halpern and Jussi Jokinen also scored for the Stars, who nearly came back from a three-goal, third-period deficit if not for Budaj, who made three enormous stops in the last minute of the game with Dallas playing with the extra attacker.
The loss snapped Dallas' 10-game season-opening unbeaten streak as well as its seven-game win streak against an Avalanche team that missed the playoffs last year despite finishing the season with a sparkling 15-2-2 mark.
In addition, the win was Colorado's first in six season-opening games against Dallas, which was unable to build off a solid 4-2-1 preseason mark.
The third-period rush, though, was much too little and much too late for Stars head coach Dave Tippett.
"We have to have the urgency before that," he said. "To win in this game you have to have the will to win, and we didn't have that many players do that tonight. We need more people that want to pay the price. Not enough guys did tonight."
After Stastny and Wolski gave Colorado a commanding 4-1 lead after two periods, the Stars stormed back in the third, cutting the deficit to 4-3 on goals by Jokinen and Hagman. But Budaj stood tall late in the game when Dallas pulled goalie Marty Turco for a sixth skater, making a big stop on Halpern's wrist shot from the right face off dot with just two seconds left.
Jokinen cut the Colorado lead in half at 7:38 of the third period when he converted with the Stars on a power play. Standing to the left of Budaj, Jokinen sent two shots to the net from close range, with Budaj making the save on the first but not the second.
Hagman made it 4-3 with a power-play goal with just under three minutes to go in regulation, banking in a pass from behind the goal line off Colorado defenseman Brett Clark's skate and past Budaj. The Stars were able to generate several good scoring chances throughout the night, but were consistently foiled by Budaj, who had a .905 save percentage last year.
But the night belonged to Stastny, who was second behind Pittsburgh's Evgeni Malkin in Calder Trophy voting for rookie of the year last season. Colorado's rising star scored his first goal of the game in the first period, beating Turco with a wrist shot from the top of the left circle, and capped his hat trick with a re-direction of center Jaroslav Hlinka's perfect pass at 11:15 of the second period.
Stastny scored his second goal of the game just one minute into the middle frame, beating Turco from the doorstep after banging home Andrew Brunette's nifty touch pass.
Brunette finished with three assists, while Hlinka had two helpers for the Avalanche, who are 8-1-3 in their last 12 home openers in Denver.
"They have some good individuals on that team and we may have given them too much space at the end of shifts," Hagman said.
Halpern cut the deficit to 2-1 with a goal seven minutes into the second. He was skating into the high slot area when defenseman Trevor Daley let go a hard blast from the right point that ricocheted of Halpern's leg and past Budaj.
The goal seemed to give Dallas some jump, but Stastny quieted the momentum with his third of the game. With Colorado on the rush, Hlinka carried the puck into the Dallas end along the right side of the ice, and found a streaking Stastny heading to the left post. Daley was unable to prevent Stastny from tapping in the perfect feed.
Wolski broke the game open when his wrist shot from the left circle beat Turco on the short side, giving Colorado a 4-1 lead with three minutes left in the second frame.
"We dodged a few bullets early and started to push back," Turco said. "Then I gave up that first goal that I didn't see clearly and it was a save I have to make. That was a momentum goal. We stayed with it and played desperate in the third period. More than anything, we have to start that way."
Halpern had Dallas' best chance late in the period, when Budaj left the net wide open after making a stop. With the puck lying in the crease, Halpern attempted to shovel it into the empty cage, but Colorado defenseman Scott Hannan was able to sprawl on the ice to prevent the attempt.
"It was frustrating to get ourselves in that position after two periods," Halpern said. "We played well but we had some turnovers that cost us. You don't want to come out for the third down 4-1. We had some guys get some big goals there but it wasn't enough."
Turco finished with 19 saves, giving a performance that Tippet wasn't very impressed with.
"We need better goaltending than we had tonight," he said.
The Stars return to Dallas to host Boston on Friday in the home opener at American Airlines Center. Game time is 7:30 on FSN.
"It is their first game and we need to be ready," defenseman Stephane Robidas said. "We have to go forward and learn from this."
This will be the first meeting between the two teams since the Stars defeated the Bruins 2-1 in a shootout at Boston on Jan. 14, 2006. Dallas is 7-2-3 in the last 12 games against the Northeast Division Bruins.
--Center Mike Ribeiro and defenseman Niklas Grossman both missed the game after being placed on the injured list on Monday. Ribeiro is still being hobbled by an ankle injury, while Grossman is bothered by a shoulder problem.
--Forwards Krys Barch and Todd Fedoruk, and defenseman Nolan Baumgartner were scratched.
--Defenseman Matt Niskanen, Dallas' 2005 first-round pick, made his NHL debut playing alongside Philippe Boucher.
--Hard-nosed forward Brad Winchester, signed by Dallas as a free agent in July, made his Dallas debut.
--Brenden Morrow was delivered a scare late in the first period when he slipped and fell awkwardly after trying to stop in the right corner. While Morrow was falling, Clark's left leg hit the Stars captain flush in the face. After a momentary delay, Morrow popped up and skated directly to the locker room while holding his hand to his mouth. He returned midway through the second period with a partial shield that covered his jaw.
--Dallas' last season-opening loss was at Winnipeg in 1995. The Jets, who are now the Phoenix Coyotes, defeated the Stars 7-5.
1 - 0 COL
2 - 0 COL
2 - 1 COL
3 - 1 COL
4 - 1 COL