John Klingberg had a goal and an assist, Alexander Radulov had two assists, and Ben Bishop made 26 saves for the Stars (23-17-4), who are 7-3-1 their past 11 despite scoring more than two goals in just three of those games.
"Keep going," Seguin said. "Not think about it. Keep that confidence and that fire and focusing on the process."
WATCH: [All Stars vs. Blues highlights]
Bishop made the save on all 12 shots he faced in the third period.
"He got it for us in the third period," Dallas coach Jim Montgomery said. "Our goaltenders have been superb, and [Bishop] is our No. 1 and he's done a tremendous job for us all year long."
David Perron scored, and Jake Allen made 15 saves for the Blues (17-20-4), who were coming off a 3-0 win at the Philadelphia Flyers on Monday but lost for the fourth time in six games.
St. Louis, which is the only NHL team that has not won the second game of a back-to-back (0-5-0), had a chance to generate momentum with two power plays in the first 5:31 but did not score on either of them.
"Power play, if you're not scoring, you've got to get momentum," Perron said. "I just thought in the third we didn't push hard enough down 3-1. It doesn't matter what happened, we've got to go and put everything out there. I know it's back-to-back, but it just felt like we should've just pushed way more. It's disappointing."