Goals by Elias Lindholm and Noah Hanifin helped the Flames rally from a two-goal, third-period deficit to force overtime, setting the table for a wildly entertaining 3-2 shootout victory.
Johnny Gaudreau did the damage in the skills competition, showing sweet hands and giving the Flames their first shootout win since Nov. 5, 2017 against the New Jersey Devils - snapping a skid of nine consecutive setbacks.
With the win, Calgary's record improves to 2-1-1 on the year.
"Obviously, I've struggled in the past with shootouts and breakaways," Gaudreau said. "It's nice for the confidence to get one there. I was going to shoot, but saw (Ben Bishop) went halfway down, so I gave him another fake-pump and brought him all the way down.
"It was a good finish. Nice to get the two points tonight."
Alexander Radulov had a chance to foil the feel-good theatre on a penalty shot with 20.9 seconds left in OT, but David Rittich made a great save to send the game to a shootout.
Rittich was diallied, finishing with 34 saves in all.
With the Flames trailing 2-0 early in the final frame, a powerplay goal by Lindholm got the visitors on the board, off the mat, and right back into contention.
On a play made possible by Mark Giordano, Lindholm rifled a long shot off the far post and in to make it a 2-1 game at 2:49 - only minutes after Stars captain Jamie Benn put the homeside up by a pair.
The Flames leveled the score with a beauty on their 20th shot of the night less than three minutes later. Hanifin followed up on a 2-on-1 between Matthew Tkachuk and Mikael Backlund, with the former sending a pass back into traffic, allowing Hanifin to walk into it and find the heart of the yawning six-by-four.
The Stars opened the scoring with 3:21 to play in the second, as a bit of a broken play off the rush turned into a partial 3-on-2.
With all kinds of time below the hash marks, the Joels - Hanley and L'Esperance - hooked up, with the former delivering a pass into the middle that was neatly tipped home at the lip of the blue paint.
Rittich had no chance on the play, stretching out with the pad to try and cut off the pass attempt, but the goal-scorer drove hard to the paint and cleverly made contact behind his left toe.
Helped, in part, by the powerplay, the Stars finished the period on a 16-9 run on the shot clock. But Rittich made several cool stops to keep his team in the game, including a ridiculous, point-blank save on Radek Faksa near the midway mark that resulted in a chorus of cheers and fist-pumps from the visiting bench in a colourful show of approval.
The Stars opened up a two-goal lead just nine seconds into the third, as Benn made short work of a Roope Hintz feed, one-timing it top-shelf on Rittich from a wide-open spot in the slot.
The goal came with a half-minute left in a Johnny Gaudreau penalty, giving the homeside their first PPG of the contest.
Cue the comeback.