Bennett made it 4-0 at 4:19, taking Tkachuk's drop pass and scoring with a wrist shot from the slot.
Sam Reinhart scored his 53rd goal of the season for a 5-0 Panthers lead at 17:56.
Tkachuk redirected a pass from Aleksander Barkov for the 6-0 final at 3:54 of the third.
"Not much needs to be said, that was embarrassing," Ottawa captain Brady Tkachuk said. "We've been down two before and we stuck with it. Tonight, different story."
Maurice got his 865th win to pass Lindy Ruff for sole possession of fourth in NHL history.
"What hits me is sometimes I think back, and I thought, 'If I could coach 500 games in this league, that would be something else,'" Maurice said. "Because I think the average number is about 250 or 350. I think you hit it and you go, 'If I could get 500 wins, that would be something.'
"And then you just start getting older. I have more fun coaching the game now than I ever have in my life. I like the game, where it's at, I really like these players in this organization, and I've been lucky. I've worked with great teams and great people and that's kind of how I got here today."
NOTES: The Panthers reached 100 points for the third time. … Florida outscored Ottawa 11-0 in two road games this season. … Maurice said forward Steven Lorentz, who had six hits in 15:48 of ice time, played through "intermittent vomiting" because of an illness that made its way through the team. … Florida forward Vladimir Tarasenko had an assist in 12:10 of ice time in his first game back in Ottawa since the Senators traded him March 6. ... Eleven Panthers players had at least one point.