DALLAS -- Kevin Porter helped the Colorado Avalanche forget that they had wasted a three-goal lead.
Chris Stewart had a goal in the second round for Colorado, but Dallas' Mike Ribeiro countered in the third.
Porter admitted he was a little apprehensive when coach Joe Sacco picked him for a turn late in the shootout, but Porter remained composed and won it with a wrist shot that beat Kari Lehtonen to the stick side.
"I was a little nervous going into it, and then Coach tapped me," Porter said. "I like to shoot on penalty shots. I saw the opening and took the shot."
Milan Hejduk had two power-play goals, and David Jones scored at even strength for Colorado.
Peter Budaj made 26 saves for the Avalanche, 5-1 in their last six against the Stars.
James Neal's power-play goal that banked in off the skate of defenseman Ryan Wilson made it 3-all at 10:02 of the third.
Adam Burish and Brenden Morrow scored 23 seconds apart in the second period to get Dallas' rally started.
Lehtonen stopped 23 shots for the Stars, whose five-game, home-winning steak ended.
On Thursday night, the Stars rallied from a two-goal deficit in the final three minutes of regulation and went on to beat San Jose in overtime, 5-4.
This time, Dallas had to settle for one point in the shootout loss.
"I was really pleased with our heart, our determination, our character, our grit," Stars coach Marc Crawford said. "Those things are good and they're continuing to define us. We persevered, got a point. You hopefully don't put yourself in that position. You find a way to win it."
The Avalanche were weary from Friday's 5-1 home victory over the New York Rangers, playing for the sixth time in nine days.
"There was a lot of things going against us tonight, but I though the character really stood out," Sacco said. "We got two points out of this game, and we're real happy with that."
Hejduk capitalized 14 seconds into the game's first power play when he steered rookie Kevin Shattenkirk's centering pass by Lehtonen at 4:05 of the opening period.
With Morrow serving the second part of a double-minor for tripping and unsportsmanlike conduct, Hejduk made it 2-0 at 3:02 of the second period with his 16th career goal -- redirecting Shattenkirk's setup.
Jones expanded the lead to 3-0 at 5:30 of the second, backhanding a rebound over Lehtonen.
Jones nearly had his second goal of the night a little more than four minutes into the third period when he skated in alone on Lehtonen, but the goalie poke-checked the puck away from him.
Burish beat Budaj from beyond the right circle at 13:33 of the second, and Morrow's close-range goal on the next shift made it 3-2.
Lehtonen was struck in the mask with a slap shot by Shattenkirk at 1:15 of the second period. Lehtonen was briefly stunned, but remained in the game after being attended to by a trainer. ... Lehtonen had the second assist on Burish's goal, the seventh of his career. ... Dallas had won its first two shootouts this season. Colorado has won both of its tiebreakers. ... The Avalanche are thin at left wing because of injuries to David Van Der Gulik (knee), T.J. Galiardi (wrist) and Peter Muller (concussion).