Hintz scored with a wrist shot on the rush at 16:49 of the third period, nine seconds after coming out of the penalty box, to tie the game at 1-1.
"I saw that they lost the puck on our blue line," Hintz said. "So I just thought that I'm going to skate towards their end. Blake [Comeau] joined with me and he gave me a nice pass."
O'Reilly scored on the rush 18 seconds later to give the Blues a 2-1 lead. It was his first goal after a nine-game goalless drought.
"It's been very frustrating not contributing offensively like I need to," O'Reilly said. "But we're finding ways to win hockey games. It's nice to contribute tonight like that. It was a great play by all of the guys on the ice to score a goal like that."
Berube agreed.
"He does so many good things without the puck, it's just a matter of time before they start going in," Berube said. "He's a great two-way player and just because he's not scoring doesn't mean he's not playing well. It was nice to see him get a goal there."
Barbashev scored into an empty net with three seconds remaining for the 3-1 final.
"I thought our whole game was pretty sound," Allen said. "Our forwards were tracking back and changing at the right times. Getting fresh bodies on at the right times was really impressive. I thought in the second period our changes were unbelievable. That makes a difference. It's little things like that that not a lot of people notice but go a long way to win games."
Colton Parayko gave the Blues a 1-0 lead at 15:41 of the first period on a wrist shot from the blue line.
"I was just trying to throw it towards the net and try to create something," Parayko said. "But there was a lot of bodies in front and it's tough for goalies, especially if you can't see me or see the puck coming at them. It's tough to get prepared for the shot."
Nathan Walker appeared to score at 15:35 of the second period in his St. Louis debut, but Dallas challenged for offside and the call was reversed on video review.
The Stars did not have a power play. The Blues were 0-for-2.
"I didn't think we did enough to draw penalties," Montgomery said. "Without the puck very much you're going to be chasing the game, so it doesn't lead to a lot of opportunities to draw penalties."