Ondrej Palat, Steven Stamkos, Alex Killorn and Dan Girardi also scored for the Lightning (27-7-2), who have gone 10-0-1 in their past 11 games. Goalie Louis Domingue made 34 saves, including seven in overtime.
Nikita Kucherov chipped in with a pair of assists. The Lightning now have a 16-0-0 record when Kucherov records a multiple-point game this season.
Johnny Gaudreau and Sam Bennett had a goal and an assist for the Flames (22-11-3), while Sean Monahan and Mikael Backlund also scored.
Making his fourth straight start in net for the Flames, goalie David Rittich made 32 saves
The Lightning opened the scoring at 3:38 of the first when Palat swatted a loose puck in the crease past Rittich. Nikita Kucherov took the initial shot from the slot that hit both Brayden Point and Monahan before bouncing right to Palat for an easy goal.