Milan Lucic, Mikael Backlund and Andrew Mangiapane scored for the Flames, while Jacob Markstrom made 23 saves.
These two teams will do battle again on Thursday right back at the Enterprise Center.
"It obviously sucks," Nazem Kadri said afterward. "That's not the way we wanted to end the game. To be quite honest, I thought we played a pretty solid road game. Had a lapse of five minutes and the good players don't need many chances to score and they made us pay.
"Got to learn from it."
Mangiapane - whose line, along with Backlund and Blake Coleman, finished with dominant possession and chance metrics - said the Blues came in waves.
"I think we sat back in the third," he said. "We didn't really do much. We sat back and they took it over from there.
"It's tough, right? I thought we were playing a decent game up until that point, but we kind of let it slip. We've got to learn from it and come back stronger against these guys next game. ... A lot of guys were saying it's like a playoff series, right? Lose this one and now we've got to even it up and win the next one here."
The Blues opened the scoring with a powerplay goal at 3:49. It was a bit of a broken play off the rush, with three of the four Flames defenders collapsing to one side of the side and opening up a lane off the rush. With a clear path to the net, Pavel Buchnevich looked for Robert Thomas for the easy, back-door tap-in, but his feed deflected off the stickoff Chris Tanev and past Markstrom for the icebreaker.
The Flames evened things up at 15:44, and what a beauty it was. With boos raining down - a callback to last year's heated playoff battle between the Blues and Avalanche - Kadri carried the puck down the left side, before feathering a scrumptious goalmouth feed to Lucic, who drove hard to the net and swatted it past Jordan Binnington.
Kadri, you may recall, has a playful history in this town that traces back to Game 3 of the Second Round last year when he collided with St. Louis goalie Jordan Binnington. It was an accident, but the Blues didn't see it that way. From a water bottle being chucked his way in a postgame interview, to the excessive, if not dangerous antics in Game 4 of that series, Kadri let his play to the talking by ignoring the vicious cross-checks and securing his first-career playoff hat-trick to quiet the critics and lead his team deeper into the spring.
In a game billed as an emotional playoff precursor, it's only fitting that one of the most legendary storylines in postseason lore was brought back to the forefront.
And Kadri would want it no other way.
"Yeah, I figured they wouldn't (forget)," Kadri said with a smile. "It's all good. I love seeing the fans engaged in the game and that's part of professional sports."
The Flames then grabbed their first lead less than two minutes later, with some considerable zone time wearing out the Blues and allowing the visitors to get a partial change in. On came Backlund in place of Kadri and after establishing good body position and taking away the eyes of the netminder, No. 11 tipped home the Nikita Zadorov point shot to make it a 2-1 game.
Richly deserved.
Shots on goal favoured the Flames 13-9 after one.
The Flames grabbed a 3-1 lead at 1:02 of the second when Mangiapane tallied his eighth of the season, going skate-to-stick and burying it upstairs over the glove. A pinching Noah Hanifin made a great feed from behind the net to make it all possible, and Blake Coleman - who's been on something of a tear lately - checked in with the second assist.
The boos, by the way, seemed to pick up steam in the second, but it didn't stop Kadri from making things happen offensively.
MacKenzie Weegar nearly extended the lead with a snapper off the far post only moments later, and Tyler Toffoli rang one off the crossbar on a late-period powerplay as the Flames continued to lean on their opponents.
For those keeping score, that's now the fourth crossbar that Toffoli has hit this year, putting him into a tie for the league 'lead' in that category. He's also hit five posts.
The Blues got some life early in the third when Markstrom mishandled a Santini shot from the near wall, allowing Nikita Alexandrov to swoop in and casually clean up the rebound. Then, just 28 seconds later, Kyrou sent a ripper from the high slot over the glove and all of a sudden, it was a 3-3 game.
With the crowd still in a buzz, Thomas converted a one-time feed from Pavel Buchnevich, but wait... The Flames challenged for offside, and the video showed Kyrou losing the handle as he entered the zone, wiping the fourth Blues goal off the board.
The Flames were out-shot 8-6 in the third before Thomas ended it on the only attempt in overtime.
"Ideally, you have a two-goal lead in the third period, you should win the game," Kadri explained. "But like I said, I don't think we gave up a whole lot and they have some great players over there that take advantage of opportunities. Played 55 good minutes tonight.
"Not enough for 60."
