Colton Parayko had a goal and assist, and Jordan Binnington made 31 saves for St. Louis, which allowed three goals and fell behind 3-1 in the first period.
"They took advantage of some opportunities they had there," said Jaden Schwartz, who scored his Blues-leading fifth goal in the playoffs. "Our puck play wasn't as good, wasn't as sharp as it usually is. They took advantage and executed on their opportunities. We did a good job climbing back, but that's a lapse we can't have."
Hintz gave the Stars a 1-0 lead at 7:11 of the first, and then there were three goals in a 1:12 span during a 4-on-4.
Miro Heiskanen made it 2-0 at 13:39 off an odd-man rush with Hintz.
"Yeah, I knew he's going to pass it," Heiskanen said. "I just drive to the net and it was great pass by Roope."