Jamie Benn had a goal and an assist, Michael Raffl assisted on both shorthanded goals, and Jake Oettinger made 35 saves for the Stars (7-7-2), who have won three straight at home and were coming off a 7-2 loss at the Minnesota Wild on Thursday.
"[Oettinger] was great," Bowness said. "He was really, really good. He's eating the puck and reading the plays really, really well. No rebounds and swallowing the puck when he had to. He reads the play really well and his anticipation is really good. He was outstanding. He's a young goalie and is going to have some ups and downs, and that goes with it, but the important thing is you see the high end."
Jordan Binnington made 29 saves, and Brandon Saad scored for the Blues (9-6-2).
"They were very hungry coming off a tough loss," St. Louis captain Ryan O'Reilly said. "They came super aggressive, and it's tough when they do that. It's tough to make clean plays, and it's not one guy specifically at fault there. It's all of us together."
Ryan Suter scored a power-play goal to give the Stars a 1-0 lead at 5:16 of the second period when his shot from the blue line beat Binnington in the top corner of the net.
"Give [the Stars] credit, they jumped on things, they were quick," St. Louis coach Craig Berube said. "It was a tight game all around. It was a tough game, there wasn't a lot of room, and they checked well. And they capitalized more than us on their chances."
The goal came four minutes after Stars forward Alexander Radulov was stopped on a penalty shot, which was awarded when Blues defenseman Colton Parayko held his stick on a breakaway chance at 1:47.
Hintz finished off a shorthanded 2-on-1 rush past a sprawling Binnington after receiving a cross-slot pass from Raffl to extend the Stars lead to 2-0 at 10:49.
"I saw that [Raffl] was skating, getting the puck, so I just tried to join with him," Hintz said. "And then I saw that there was only one [defenseman] in the play, so it was good. … It's a big one that you get [the pass] on the tape because you're trying to skate fast, so if it's not there, it might be a missed chance, but today I got two nice passes, so it was great."