From there, it was all Calgary in the opening 20.
The Flames took their first lead at 8:39 after Winnipeg defenceman Josh Morrissey turned the puck over in the worst place possible, giving the homeside a clean look from the hash marks. Tkachuk dished off to Bennett at the edge of the left circle, and No. 93 whipped it high over Hellebuyck's right shoulder, giving him goals in back-to-back games.
Then, Tkachuk took matters into his own hands and put the Flames up by two on a fortuitous tally at 11:35. With speed off the rush, Tkachuk fired a long-range missile that Hellebuyck waved at and got a piece of with the glove, but it skipped it through tumbled behind him.
Hellebuyck's night came to a premature end, as the Vezina finalist was pulled after allowing three goals on nine shots. He was replaced by former Flames draft pick Laurent Brossoit between the pipes.
"You have the game pretty much won right there if you play good defence [the rest of the night]," Tkachuk said. "You've got to bear down. They were down - I know it sounds funny - only four goals, and with a team like that?
"They got a couple right away. We had to be careful. Play a little bit safer, for sure, but we had to play the exact same way in the third as we did in the first."
Which was, in a word: Dominant.
Jankowski went back to work in the dirty areas and after winning a puck battle deep in enemy territory, he took it hard to the net, wrapped it through the blue paint and banked it off the left skate of Jets defenceman Tyler Myers to give the Flames a 4-1 lead.
Gaudreau rounded out the first-period scoring with a beautiful strike at 19:13, beating the netminder with a laser top shelf, blocker side.
The Jets were all over the Flames in the middle frame, outshooting the homeside 17-3, on the strength of three powerplay chances.
The Jets finally solved Rittich with 14 seconds to play at the tail end of their third man-advantage, as Patrik Laine shredded a one-timer into the open cage after getting a terrific feed from Blake Wheeler.
Laine ripped home his second of the night on a powerplay 6:17 into the third to cut the deficit to two. Elias Lindholm had a chance to clear it moments earlier, but stick failed him at the most inopportune time, keeping the play alive at the Calgary blueline.
"Best team we've played this year, easily," Tkachuk. "It starts with their D, and they get the puck up so well. Their stars up front are awesome. Their goalie has played well this year, too and that's why we needed to get pucks on him early, and we did and we got bodies there.
"When you want into the room after the (first) period we had, it feels good."
With the win, the Flames have picked up six of a possible eight points on the homestand, and have now won eight of their last 11 overall.
The Flames will now head out on a two-game road trip beginning on Friday in Vegas.
"This homestand was big for us," Tkachuk said. "We wanted to come in here and not change our season, but elevate our game at home so we can bring it on the road. I don't think we've been as good as we've wanted to be on the road ...
"But it started with homestand, elevating our game."