Markus Granlund scored the only goal of the shootout in the eighth round, and Jacob Markstrom made 38 saves for Vancouver (34-35-10), which has been eliminated from playoff contention.
Granlund won it with a backhand deke that went five-hole on Khudobin.
"They're a good team and they've got a lot to play for," Markstrom said. "It doesn't matter where you are in the standings, they're all going to be competitive games. You want to win."
Tim Schaller, who scored his first two goals of the season in Dallas on March 17, jammed in a backhand between the left post and Khudobin's pad from behind the net to give the Canucks a 1-0 lead at 4:52 of the first period.
After a turnover by the Stars in the neutral zone, Sven Baertschi skated down the right wing and scored with a wrist shot five-hole on Khudobin from low in the right circle to make it 2-0 at 11:16.
"It felt great. It's been a long time," said Baertschi, who was playing in his third game since missing 23 because of recurring symptoms from a concussion. "I saw [Elias Pettersson] on the other side and I think he has enough goals this year so I just shot it myself."