Ryan Lomberg made it 4-2 at 19:43 of the second period with a low shot from close range.
Hornqvist extended the lead to 5-2 at 5:47 of the third period with a wrist shot from just outside the right face-off dot. Lucas Carlsson scored at 13:04 for the 6-2 final.
"You give up that many goals, you're not going to win," Flames coach Darryl Sutter said. "We had some defensemen that weren't into the defending or checking part of the game and it cost us the hockey game."
Bobrovsky, who started three of four games during the homestand, made 35 saves over the last two periods.
"'Bob's' great," Lomberg said. "He played how he can. We've got all the confidence in the world in Bob and in our goaltending, so it's no surprise to us in our room when he makes big saves and does it time and time again. There's no surprise. We see it every day from him."
NOTES: The Panthers are 19-0-0 this season when they score at least four goals. … Florida was without former Calgary center Sam Bennett, who served the first of a three-game suspension for an illegal check to head against Montreal Canadiens forward Cedric Paquette on Sunday. … Duclair has scored four goals in his past four games. … Thornton's goal was his 548th NHL power-play point, moving him past Larry Murphy for 20th in NHL history. … The Panthers' 20 goals are their most in a three-game span (excluding shootout-deciding goals). The previous high was 18 from Feb. 5-9, 2008. … Flames forward Brett Richie had two shots on goal in 10:39 of ice time in his first game since Nov. 2, when he sustained a lower-body injury against the Nashville Predators.