Brayden Schenn scored for the fourth straight game for the Blues (39-17-10), who lead the Colorado Avalanche by three points for first place in the Central Division. Jake Allen made 28 saves through overtime and three more in the shootout.
Allen made the save against Jamie Benn on a breakaway with 59 seconds remaining in overtime.
"I tried to have some fun with it," Allen said. "We've been in a lot of overtime games this year. I can't put a number on it, but quite a few and, you're not going to win them all, honestly. It's a pond hockey game, so you're just waiting for a breakdown, and they got one there. I thought it was going to be 2-on-0 originally, and then Benn sort of pulled away, got the save, and Ryan] O'Reilly had a big goal in the shootout."
***[WATCH: [All Stars vs. Blues highlights]*
John Klingberg tied the game 3-3 for Dallas with 19 seconds left in the third period and goalie Anton Khudobin pulled for an extra attacker.
"I think we have a really good system 6-on-5, and we stuck with it," Klingberg said. "I think we hold on to the pucks there and take what's open. We knew that they were going to try to pack it in when they play 5-on-6. We got some opportunities there, and credit to the guys down low. They won back the pucks, and that's how you create scoring chances."
It was the second straight loss for the Stars (37-21-7), who trail the Avalanche by four points for second in the Central.
"I always look at these shootout losses as you don't lose the game, because you don't lose the game, you tie the game," Dallas coach Rick Bowness said. "You lose the shootout. We played with them. It was great to see us come back because I thought we were playing really well."