Talbot, Colorado's 11th shooter, beat Stars goaltender Kari Lehtonen far post to win it for the Avalanche (22-18-11), who trailed 2-0 after two periods. It was Talbot's first career attempt.
"First time, first time shootout," Talbot said. "I had two penalty shots in my career; 100 percent (in the shootout). I was 1-for-2 in penalty shots."
Colorado defenseman Tyson Barrie scored an extra-attacker goal with 20 seconds remaining in the third period to tie it 2-2.
"It's an important win for us, especially the way they played in the first two periods," Avalanche coach Patrick Roy said. "They were really sharp and they didn't give us much. Every time we had some good looks, they had great stick. They blocked some of our shots, but I thought their game was A-1 tonight. It's nice to rally after giving up that late goal in the second period. Our guys showed some character."
Dallas could have won after the shootout goals by Roussel and Sceviour, but Briere and Landeskog scored on Lehtonen in the eighth and ninth rounds.
"Just having those two opportunities to stop the last one, and I wasn't able to get those, I was disappointed at that," Lehtonen said.
"You can't play any better and lose," Stars coach Lindy Ruff said. "We gave up nothing for 60 minutes. They had maybe five chances. The puck just can't get through us at the end [of regulation]. That's just a tough one. We had two opportunities (to win the game) in the shootout and didn't. It hurts."
The Stars (23-19-8) took advantage of the game's first power play when Patrick Eaves scored his sixth of the season 6:47 into the first period. Eaves received a pass from Dallas captain Jamie Benn inside the right circle and snapped the puck into the upper left corner.
Dallas was on the power play after Seguin drew a hooking call on John Mitchell at 6:27.
Colorado didn't get its first shot on goal until 7:23 into the period when O'Reilly attempted to score on a wraparound.
Dallas' Cody Eakin had a breakaway 6:16 into the second period when the Stars were shorthanded, but his wrist shot from the slot sailed left of the net.
Dallas went ahead 2-0 with 52 seconds remaining in the second when Cole scored his 13th of the season. Avalanche defenseman Nate Guenin was attempting to clear the puck but instead sent a pass right to Stars forward Ales Hemsky, who flipped the puck to Cole with a backhand. Cole, playing his first game since missing the past three because of an upper-body injury, scored from the slot.
"Everybody makes mistakes," Roy said. "You think I never made mistakes? I remember one in the playoffs in 2001. It's part of the game and how you bounce back. That's what you want to see as a coach, and we have a lot of confidence in our players and we're certainly not going to punish them because they make a mistake."
O'Reilly scored 6:12 into the third period after a slap shot from Brad Stuart deflected off the boards behind the net and the carom fell at his skates near the far post. O'Reilly tapped in the puck for his 10th goal of the season.
Varlamov headed to the bench with 1:47 remaining and Colorado scored when Barrie's slap shot from the right point first hit Lehtonen's stick and then traveled through his five-hole for Barrie's fifth goal of the season.
"Tonight was a huge character win I think, coming from behind and winning in this barn against a pretty good team," Talbot said.
Varlamov robbed Seguin at the near post 3:17 into overtime with a glove save as he tried to score from the edge of the right circle off a faceoff. Colorado outshot Dallas 9-1 in overtime.
"I thought we did some good things in the third there," Eaves said. "They got a fortunate bounce, and then one with the extra man. It was a shootout loss. Obviously, we're disappointed."