Parayko's hard shot from the slot hit Ben Bishop's left shoulder, knocking the goalie onto his back and deflecting the puck to deep in the circle. Alexander Steen took a shot from there that was redirected by Jaden Schwartz over the still laid-out goalie in a 4-1 victory to force Game 7 in the second-round Western Conference semifinal series.
"That's a hard shot. A really hard shot. Shoot the puck, right? It's a great play by (Steen) to put it right back on the net," Blues captain Alex Pietrangelo said. "Great job Schwartzy. He's been around that all series long and keeps getting rewarded."
Schwartz's eighth goal of the playoffs with 12:23 left made it 3-1, and was the first of two goals by the Blues in a 33-second span.
Bishop was tended to by a trainer and initially stayed in the game, but a switch was made soon after when Sammy Blais, playing his first postseason game, got a slap shot past him.
"When you're right there in the slot, and you're going to try to shoot to score," Parayko said. "Obviously I just try to get it around that first guy and find a corner. ... I'm never out there to hurt anybody."
Stars coach Jim Montgomery said Bishop was fine, pointing out that he had stayed in the game before Anton Khodobin got his first action of the postseason.
While St. Louis maintained possession of the puck while Bishop was down, Stars defenseman John Klingberg thought there should have been a whistle to stop play.
"We can't change anything right now," Klingberg said. "We didn't play good enough to win. It's not like we're focusing on that right now."
Blues coach Craig Berube said officials "don't blow the whistle when you have possession. ... His mask was still on, so that's the reason."
Pietrangelo scored only 63 seconds into the game and David Perron also had a goal for the Blues, who will be on home ice for the deciding game Tuesday night.
The Central Division rivals also went to a Game 7 when they met in the second round three years ago. That series finale was played in Dallas, where the Blues scored three times in the first period and went on to a 6-1 win.
St. Louis rookie goalie Jordan Binnington stopped 22 shots, allowing only a power-play goal by Tyler Seguin in the first period.
Bishop, who came into the game with a .936 save percentage in the playoffs, allowed four goals on 20 shots. Khodobin had five saves in the final 12 minutes.
The two quick goals by St. Louis came right after Dallas couldn't score with Binnington sprawled on the ice.
Perron put the Blues ahead to stay at 2-1 with an interesting goal in what was otherwise a somewhat pedestrian second period.
Oskar Sundqvist skated deep into the right circle and passed back across the front of net. Perron, with Klingberg between him and Bishop, reached his stick around the defender to poke the puck in for his third goal of the playoffs.
"I'm ready to turn the page and move on to the next game. It was an exciting challenge for us," Perron said. "None of the guys came in here with their head between their legs. I just thought we were ready for the challenge. ... We're just excited to keep playing hockey."
The Stars' 23 shots matched their fewest in the playoffs. Their goal came with 8:25 left in the first period when Mats Zuccarello made a pass from the top of the right circle and Seguin's shot got under Binnington and trickled past the line to make it 1-1.
St. Louis had eight shots on goal before Dallas finally got its first nearly nine minutes into the game. The Stars then went nearly seven minutes before their first shot of the second period.
NOTES: St. Louis is 5-1 on the road in the playoffs, its most wins away from home in a single postseason. ... The Blues have scored 18 third-period goals this postseason, the most among the playoff teams. "I think we're wearing teams down through games," Pietrangelo said. "I think the way we play is hard to defend." ... The Blues are 29-41 when facing elimination in best-of-seven series, 11-26 on the road. Dallas dropped to 25-20 in potential clinchers, 13-7 at home. ... It was 11 years ago Sunday that Dallas finished a four-overtime win in Game 6 over San Jose (the game started on May 4, but ended after midnight on the May 5) to wrap up that second-round series. That had been the last time the Stars clinched a playoff series at home before their Game 6 win over Nashville in the first round this year.
The deciding Game 7 is Tuesday night in St. Louis.