The Flames remain en fuego through five straight games after defeating the best team in the league on their home ice.
Traveling to the Amalie Arena to face the Lightning for the first time this season, Calgary handed Tampa Bay one of just four home losses this season.
Mike Smith made 33 saves on 34 shots, while Johnny Gaudreau, Mark Jankowski and Michael Ferland each added a goal and an assist. Sam Bennett and Matthew Tkachuk scored a goal apiece.
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Lightning defenseman Victor Hedman did not return after a knee-to-knee collision along the boards in the second period. He will be reevaluated Friday for a lower-body injury.
Despite trailing the Lightning 24-34 in shots on goal, the Flames overcame Vezina Trophy favorite Andrei Vasilevskiy, who leads NHL goaltenders in wins with 27 and shutouts with six on the season.
The Lightning have four players on the Atlantic Division All-Star roster. Captain Steven Stamkos, top scorer Nikita Kucherov and defenseman Victor Hedman will join Vasilevskiy, while the Flames will send their own "Johnny Hockey" to his fourth career All-Star game.
Tampa Bay goes into its six-day bye week leading the league with 65 points and a 31-10-3 record. The Flames will continue their roadtrip Jan. 12 to take on the Florida Panthers.