A victory Thursday against their former archrival, the Detroit Red Wings, would tie the franchise record of seven wins in a row to begin a season set by the Quebec Nordiques in 1985-86.
"This is what we've been doing since the start of the year -- finding a way to win," Avalanche coach Patrick Roy said. "There's nights where we've played better. Tonight was not our best game. I think the main reason is we didn't manage our game well. We made turnovers at the blue line that cost a lot of chances. We didn't get the puck out of our zone. That also created some chances, and we took some penalties."
Matt Duchene scored two goals to reach the 200-point mark for his NHL career and goalie Semyon Varlamov made 39 saves, including one against Alex Chiasson just before the final buzzer to preserve his fifth win.
The Avalanche iced the puck with 2.3 seconds left and Chiasson jabbed at the puck just outside the crease after the ensuing faceoff.
"That was a scary moment for me because they almost scored," Varlamov said. "I remember three years ago when I played in Washington there were five seconds left when I got scored on. Tonight, I'm thankful they didn't score."
Duchene put the Avalanche in front 3-2 at 14:18 of the second period during a delayed penalty. Duchene accepted a return pass from PA Parenteau in the neutral zone, where he skated by Stars center Tyler Seguin, continued into the left faceoff circle and launched a shot that beat goalie Dan Ellis to the far corner.
"When I got the puck I knew they were tired," Duchene said. "I tried to work a give-and-go with PA. He's one of the best give-and-go players in the League. We've done that a hundred times, so it was nice to find him. He found me back and they were all tired and I had a fresh set of legs."
Varlamov also made a big stop against Seguin at 7:25 of the third period during the Stars' fourth power play of the game.
"I guess goaltending is crucial in this League," Roy said. "You need some great goaltending every night and that's what we've been lucky with. We've had great goaltending since the start of the year, but we have to be better in front of them. Tonight, let's remember that one. That's a game where I think Varly stole it and we need to be better in some areas of the game."
The Stars tied the game 2-2 at 10:58 of the second period on a power-play goal by Cody Eakin with one second left on Nathan MacKinnon's hooking penalty. Eakin scored with a shot from low in the right circle. It was the first goal allowed by the Avalanche in 14 shorthanded situations this season.
The Stars outshot the Avalanche 18-5 in the period with seven of the shots coming on three power plays. They finished with 11 power-play shots for the game.
"We really dominated the play chart," Stars coach Lindy Ruff said. "The second and third periods the opportunities were there. The opportunities were created, even the penalties, were created from skating. It was probably our best skating game, probably our best game on a chance sheet and Varlamov came up with some beauties."
Said Stars captain Jamie Benn: "He’s been doing it all year. He played another great game and sometimes you have to give them credit."
Roy said Tuesday morning that his team needed to do a better job reducing the number of opponents' shots and scoring chances, especially in the second periods of games. The Avalanche have been outshot 52-18 in their past three second periods.
"Obviously tonight there are some details in our game where I was not too happy and we're going to have to fix," Roy said. "The good thing is we can fix it (while) winning."
The Stars opened the scoring at 4:18 of the first period on a breakaway by Rich Peverley, who skated between Avalanche defensemen Nate Guenin and Ryan Wilson before firing the puck between Varlamov's pads.
The Avalanche tied the game at 11:43 on Duchene's first goal, which came on an open shot from the left circle that sailed by Ellis' right arm.
Varlamov stopped Stars defenseman Trevor Daley on a breakaway after he exited the penalty box at 17:22 and he thwarted Chiasson on the doorstep 52 seconds later.
The Avalanche went ahead 2-1 with seven seconds remaining in the period on a goal by defenseman Jan Hejda, whose shot from the high slot slid through a crowd of bodies in front of Ellis.
The win enabled Roy to tie Mario Tremblay's record for consecutive wins by a head coach to begin his NHL career. Tremblay won his first six games with the Montreal Canadiens -- Roy was the team's top goalie -- in October 1995. Two months later, Roy wasn't pulled from a game against the Red Wings after allowing nine goals. He stormed past Tremblay on the bench and a few days later was traded to the Avalanche.
"I don't know what to say. It doesn't happen to me very often," Roy said of the ironic twist. "It's not something that I'm looking at, to be honest with you. I certainly appreciate more the way our guys are playing than breaking a record like this. I'm not really excited about that record. I'm excited about looking at the way the team has been playing and how hard the team has been working."