Opening the scoring against his former team, Brandon Montour, who suited up in Buffalo from 2018-21, slid down from the blue line, picked up some loose change in front of the net and fired a shot past Ukko-Pekka Luukkonen to give the Panthers a 1-0 lead at 4:01 of the first period.
Earning an assist on the goal, Tkachuk extended his point streak to seven games.
"You've obviously just got to pick your spots, especially against a team like this that's fast and skilled," Montour said. "They cheat for offense. There was just a play there where I found an open lane, and Chucky found a lane to get it to me. I got the rebound and it was good."
Keeping up the pressure in the second period, the Panthers added to their lead when a pass from Carter Verhaeghe deflected off Tkachuk in the slot right onto the stick of Sam Bennett, who then beat Luukkonen with a nice shot from the right circle to make it 2-0 at 8:04.
Through two periods, Florida led 29-16 in shots on goal.
"Sergei made a bunch of really important saves, and then I thought we played a smart game in the third," Panthers head coach Paul Maurice said. "We didn't give up anything on the odd-man out. There was 10 minutes in the first where it was loose, but after that we were pretty tight."
Just 34 seconds into the third period, the Panthers gave themselves more breathing room when Sam Reinhart teed up Anton Lundell for a one-timer with sweet dish on a 2-on-1 rush to make it 3-0.