Tkachuk, who played eight seasons with the Senators, including five as captain, had a goal in his first game in Ottawa since being traded to Florida on June 21.
Claude Giroux, Shane Pinto and Warren Foegele scored for the Senators (7-3-0), who have won two of their past three games. Linus Ullmark allowed one goal on 17 shots before exiting at 3:25 of the third period with a lower-body injury. Samuel Ersson made one save in relief.
Jake Sanderson had two assists in his return to the lineup after missing the past eight games with a lower-body injury he sustained in Ottawa's season-opening 3-2 win at the Toronto Maple Leafs on Oct. 3.
Akira Schmid made 25 saves for the Panthers (5-3-2), who had won three straight, and will face the Pittsburgh Penguins in the second game of a back-to-back on Thursday.
Brady Tkachuk scored on Florida's first shot of the game to make it 1-0 at 10:00 of the first period on the power play. He received a pass from his brother Matthew down low on the right side before putting a wrist shot under Ullmark's right arm.
Stutzle tied it 1-1 with a power-play goal at 14:13. Sanderson fed a pass to Stutzle in the right face-off circle, where he one-timed it into an open net.
Giroux gave the Senators a 2-1 lead at 9:34 of the second period, burying a wrist shot past a screened Schmid from between the circles.
Pinto pushed the lead to 3-1 at 17:18. He caught a pass in stride from Sanderson, powered past Panthers defenseman Niko Mikkola into the offensive zone, and had the puck deflect off his skate after an attempted deke before it trickled in under Schmid's right pad.
Foegele put the Senators up 4-1 while short-handed at 7:58 of the third period. Dylan Cozens made a slick move around Florida defenseman Sandis Vilmanis to set up Foegele at the edge of the left circle, where he snapped the puck five-hole.
On a short-handed rush, Halliday took a drop pass from Stutzle and lifted a shot over Schmid's glove from the right circle for the 5-1 final at 14:57.
