Colton 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.
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.
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.
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 the 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.
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.