Ondrej Palat, Steven Stamkos, Alex Killorn and Dan Girardi scored in regulation for the Lightning (27-7-2), who improved to 10-0-1 in their past 11 games.
Domingue stopped each of the seven shots he faced in overtime. He allowed one goal to Sean Monahan in the shootout.
“I like our chances every time we go to extra time,” Domingue said. “We’re a pretty good team. That’s what makes us such a good team. We find ways to win games. It doesn’t matter how. We take the two points and run.”
Girardi said Domingue won the game for the Lightning.
“He made some huge saves, back-to-back on Monahan (in overtime),” he said. “It was too many to really count. He was huge for us — in the shootout as well, making some big saves.”
Nikita Kucherov added two assists. Tampa Bay is 16-0-0 when Kucherov records a multipoint game this season.
Johnny Gaudreau and Sam Bennett each had a goal and an assist for the Flames (22-11-3), who led 3-1 after one. Sean Monahan and Mikael Backlund also scored.
Making his fourth straight start, Calgary goalie David Rittich had 32 saves.
The Flames fell behind 3:38 into the first when Palat swatted a loose puck past Rittich. But they put together an impressive response.
Bennett tied it 51 seconds later with a tap-in goal of his own. Domingue got a piece of Bennett’s first shot, but the puck trickled behind him and the Calgary forward adeptly followed up on the play.
Monahan put Calgary in front at 7:50 when he muscled his way into the slot past Tampa Bay defenseman Braydon Coburn and one-timed a pass from Elias Lindholm past Domingue.
Backlund then was the beneficiary of some hard work by Bennett 12:25 into the first. Bennett fought hard behind the net to get the puck out front to Backlund, who backhanded his linemate’s pass past Domingue.
Stamkos scored his 18th goal of the season at 3:19 of the second when his pass to teammate Adam Erne went off Calgary defenseman TJ Brodie and past Rittich.
Killorn then swatted a rebound in behind the Calgary goalie at 5:52, tying it at 3.
After Girardi blasted a point shot past Rittich at 15:35 of the third, Gaudreau backhanded a shot through Domingue’s legs at 17:32 to tie things up once again.
“I found a way to tie it up and we played really well in overtime,” Gaudreau said. “I thought we had a lot of really good looks — all three pairs or trios. It’s unfortunate, but it was a good game. I’m sure it was entertaining for the fans and it was fun to play in that game.”
NOTES: Playing in his 700th NHL game, Stamkos scored his 366th goal to pass Martin St. Louis for second on the club’s career list. Stamkos trails just Vincent Lecavalier (383) for most goals in team history. … Bennett and James Neal returned to Calgary’s lineup after being sidelined by upper-body injuries. Bennett missed a pair of games, while Neal sat out on Saturday in Dallas when the Flames lost 2-0 to the Stars.