Rasmus Andersson, Jonathan Huberdeau, Tyler Toffoli and Andrew Mangiapane each had a goal and an assist, and Brett Ritchie also scored for the Flames, who improved to 5-4-1 in their last 10 games. Dan Vladar made 30 saves.
Nick Cousins and Sam Reinhart scored for the Panthers, who dropped to 3-4-3 in their last 10. Sergei Bobrovsky stopped 17 of 23 shots.
Tkachuk spent his first six NHL seasons with Calgary and was traded to Florida this summer. The 24-year-old was a restricted free agent and told the Flames he would not sign long-term with the team. Calgary got Huberdeau, defenseman MacKenzie Weegar, prospect Cole Schwindt and a conditional draft pick from Florida.
Tkachuk was booed Tuesday whenever he touched the puck, but also received a partial standing ovation during a video tribute to him early in the first period.
''Just passionate fans here,'' Tkachuk said. ''It's obviously nice to see that video.
''A couple seconds of showing what my time was like here on and off the ice, it was nice to see.''
During the third period, Flames fans chanted ''Hubie's better!''
''I didn't hear that. That's kind of funny, obviously,'' Huberdeau said.
He was chosen the first star of the game.
''He's a hell of a player,'' Andersson said. ''At the end of the day, it's a hockey trade and it's a trade that works out for both teams. We get Weegsy and Hubie who are (terrific) players and Florida gets a really good player as well.''
Huberdeau scored in the shootout when the Flames edged his former team 5-4 on Nov. 19 in Florida.
''I'm glad it's over the year and now we can just focus on the season,'' he said.
After scoring three unanswered goals in the opening period, the Flames led 4-2 heading into the third.
Mangiapane and Dube combined on a second goal on an odd-man rush with Mangiapane finishing it at 18:54.
Bobrovsky stopped Huberdeau on a breakaway with just under five minutes to play, but Huberdeau collected the loose puck and fed Toffoli for a one-timer from the hash marks at 15:22.
Both goalies gave up soft goals in the second period. Reinhart's low shot off the rush from the top of the faceoff circle beat Vladar's outstretched glove at 16:55.
Ritchie's sharp-angled shot on a rebound tied up an out-of-position Bobrovsky at 15:29.
Trailing 3-0, the Panthers struck early in the second when Cousins redirected Gustav Forsling's pass at 9:54.
Andersson scored Calgary's third goal at 13:03 of the opening period. When Bobrovsky gave up a long rebound, the Flames defenseman got inside position on Florida's Aleksi Heponiemi to get a shot away.
Huberdeau got on his stick on a rebound during a goal-mouth scramble. The puck deflected off legs and sticks and found its way into the net for a power-play goal at 9:21.
Dube's backhand redirect beat Bobrovsky on a 2-on-1 with Mangiapane for a short-handed goal at 3:05.
The Panthers were without captain Aleksander Barkov for a third straight game because of a non-COVID-19 illness. Barkov has five goals and 13 assists in 19 games this season.
''Feeling better today, which is the first kind of positive news,'' coach Paul Maurice said before the game. ''We hope he's on the mend here. Don't have a timeline for it, but we are more confident and feeling better about where he's at than we were yesterday.''
Florida: At Vancouver on Thursday in the third of a five-game trip.
Calgary: Host Montreal on Thursday in the second of a five-game homestand.
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