Dillon Dube and Rasmus Andersson also scored for the Flames, and Cam Talbot made 31 saves for the shutout.
Calgary’s Milan Lucic set the tone when he fought Nathan Beaulieu right after the opening faceoff and beat the Jets’ defenseman.
“I was lining up for the draw and he came over and asked me,” said Lucic. “He’s trying to show that they’re ready to play and that they’re not going to go down without a fight.
“For me, you just want to show that you’re ready to play and you’re not going to back down from their push.”
Connor Hellebuyck stopped 30 shots for the Jets.
Calgary outscored Winnipeg 16-6 while winning three of the four games. It was a series the Jets were chasing from the get-go, when they lost elite scorers Patrik Laine and Mark Scheifele to injury in Game 1. Two other top point-getters Blake Wheeler and Kyle Connor failed to step up to fill the void.
Wheeler and Connor (the regular season team leader with 38 goals and 73 points) combined for just two assists in the four games.
Wheeler said the loss of Laine and Scheifele was critical.
“The guys that played this series, there’s nothing left in tank,” he said. “Our team left it all out there. … Their goalie made some big saves, and it just wasn’t meant to be.”
Calgary, meanwhile, had scoring up and down the lineup and kept the Jets on their heels for the most part with a relentless forecheck.
Dube got the Flames on the scoreboard 3:21 into the game. Battling in front of the Jets’ net against Nicholas Shore, he got off a shot that Hellebuyck stopped. However, Dube got his own rebound and flipped it up and in.
The Jets outshot Calgary 11-8 in the period, but went down 2-0 with less than a second to go when Bennett pounced on a rebound off an odd-man rush to knock the puck past Hellebuyck.
The Jets made sporadic attempts over the final two periods to get back in the game, only to have Talbot shut the door.
Monahan and Andersson scored empty-net goals in the dying minutes to seal the victory.
“Just being able to lock it down in that game, that’s a big step for our group and just being ready for the next round, being able to withstand their push,” Dube said.
There were 11 different goal scorers for Calgary in the four games: Mikael Backlund, Elias Lindholm, Johnny Gaudreau, Bennett, Dube, Milan Lucic, Matthew Tkachuk, Monahan, Tobias Rieder, Andersson and Andrew Mangiapane.
It was the only all-Canadian matchup of the eight qualifying series.
Calgary won the opener 4-1, lost Game 2 by a 3-2 score, then rebounded to beat Winnipeg 6-2 in Game 3. The games were all played without fans in the stands at Rogers Place, which is hosting the Western Conference tournament, keeping players in isolation to avoid contracting COVID-19.
Calgary is the first team through in the expanded Western Conference and will play one of the top four seeds in the round of 16: the Colorado Avalanche, St. Louis Blues, Dallas Stars or Vegas Golden Knights.
Cam Talbot made 31 saves for his third NHL postseason shutout and first since April 16, 2017, for the Edmonton Oilers.
“This is just one step in the big picture,” said Talbot, who got his third career postseason shutout. “We knew this was going to be a hard-fought series, and I think we’ll be better for it playing in the qualifying round. We’re going to be a little bit more battle-tested.”
The Flames were the eighth seed, finishing the truncated regular season at 36-27-7 (.564 winning percentage). The Jets were seeded ninth (37-28-6, .563).
Calgary will get a chance to redeem a crushing first-round playoff exit last spring at the hands of the Avalanche despite topping the Western Conference with 50 wins in the regular season.
There was also controversy and disruption in November, when Geoff Ward was promoted from associate to interim head coach after Bill Peters resigned amid allegations of misconduct, including directing racial slurs at a player when he was a coach in the American Hockey League.
Goaltending was a question mark heading into the series, but Talbot, understudy to David Rittich in the regular season, outplayed him in the exhibition game before the tournament and played every minute in the series.
The tenor of the series shifted dramatically in the first five minutes of Game 1, when Scheifele (29 goals, 73 points in the regular season) got his leg twisted up with Tkachuk along the boards, and fell to the ice in pain and had to be helped off.
Jets head coach Paul Maurice said Tkachuk was deliberately trying to injure Scheifele, something Tkachuk denied.
Laine later appeared to injure his wrist and bottom-six forward Mason Appleton was also hurt and never reappeared in the series.