ST. PAUL, Minn. -- Milan Hejduk's 37th birthday was marked by a victory and a milestone.
Hejduk also scored in regulation to record his 800th career point.
"A couple guys asked me this morning what I want for my birthday. I said I'd like to get a win and put a smile on everybody's face in the locker room which happened, so that's cool," Hejduk said.
The loss ended a three-game slide.
Hejduk beat Niklas Backstrom with a backhand move and Duchene beat the Minnesota goaltender with a wrist shot.
"I had no idea where I was going to go really. I just tried to outwait him a little bit and put it behind him," Hejduk said.
Duchene and Aaron Palushaj also scored in regulation for Colorado. It was the first shootout of the season for the Avalanche.
"A lot of good things in our game tonight, but most importantly the two points which we wanted," coach Joe Sacco said. "Our guys fought hard tonight; they had to battle for every inch of ice out there. When you do that usually you get rewarded."
Minnesota coach Mike Yeo had far different feelings about his team.
"It was there to be taken, if you do the things to take it. There was a lack of urgency, I would say, in a lot of areas," he said choosing his words carefully. "I don't think we were prepared to play the right way."
Parise, Koivu and Mike Rupp scored for Minnesota, which netted three goals for the first time in seven games. The Wild has 10 goals in that span.
"This was a game we needed to win. The plus side is we got a point, but you can't find any contentment in that," Rupp said.
Hejduk became the fourth player in franchise history -- second in Colorado -- to reach 800 career points.
The only other Quebec/Colorado players to reach that number were Joe Sakic (1,641), Peter Stastny (1,048) and Michel Goulet (945). Hejduk has 13 career power-play goals against Minnesota, the most of any Wild opponent.
"I got 1,000 games like four games ago and now 800, so it's really cool," Hejduk said. "But I really don't focus on the stats right now. I just want to keep focusing on the team and how we do."
Minnesota entered the game as the league's second-lowest scoring team at 1.92 goals per game; Colorado the third-worst at 2.09. So by their standards, the third period was practically a barrage of goals.
Minnesota was trailing 2-1, when Rupp tied it early in the third by taking a pass from Mikael Granlund at the right post and whacking it past Giguere on the second try.
Koivu gave Minnesota a 3-2 lead at 11:56, picking up a loose puck in the Colorado slot, switching to his backhand and lifting a shot over the glove of Giguere.
Duchene answered 46 seconds later, when from behind the end line, he banked a shot off sliding defenseman Jared Spurgeon and the puck ricocheted into the Wild net.
Parise answered midway through the frame on wraparound after Giguere failed to control a rebound of a shot by Koivu. Dany Heatley also had an assist.
In an effort to find some offensive production, Yeo has reunited the top line of Parise, Koivu and Heatley after being apart for a little more than a week. Entering the game, Parise had one goal in the past eight games, Koivu had one assist in his past seven and Heatley was pointless in the past eight.
The trio finished with 13 of Minnesota's 29 shots, including nine by Parise.
Hejduk scored a power-play goal late in the second period for a 2-1 Avalanche lead, putting a rebound of a slap shot by Jamie McGinn over the stick-side shoulder of Backstrom.
Backstrom is 21-5-3 all-time vs. Colorado ... This was just the third time in 12 games that the Avalanche scored first. ... Minnesota has reassigned forwards Charlie Coyle and Matt Kassian to AHL Houston. ... Wild forward Pierre-Marc Bouchard, who has three points in 11 games, returned to the lineup. He was a healthy scratch Tuesday in Vancouver. ... Colorado D Matt Hunwick, who missed Monday's game with a torso injury replaced Erik Johnson, who suffered a head injury Monday and is out indefinitely.