Nick Paul and Brady Tkachuk scored two late power-play goals, and Drake Batherson had a goal and two assists. Tim Stutzle, Dylan Gambrell and Austin Watson also scored for Ottawa. Connor Brown had three assists.
Sam Reinhart and Jonathan Huberdeau scored for the Panthers, who lost at home for only the second time this season. The Senators have won five of six.
Florida goaltender Spencer Knight gave up a career-worst eight goals on 38 shots.
It was the Panthers' worst home loss since falling 7-1 to Philadelphia on Jan. 26, 2013, and their worst overall since a 6-0 beating at Calgary on Jan. 13, 2016.
The Panthers went 0-6 on the power play, including 27 seconds of a 5-on-3 in the third.
With the score tied at 2, the Senators scored two goals in a span of 80 seconds late in the second period.
Norris' shot from the slot beat Knight on the stick side at 16:06, and then Stutzle fired the puck from the high slot that went high into the net.
Norris' second goal 23 seconds into the third made the score 5-2 and Batherson made it 6-2 with 13:50 left.
Paul concluded the scoring with his second goal with 5:03 left.
Gambrell's short-handed goal on a breakaway gave the Senators a 2-1 lead with 18:30 left in the second.
The Panthers tied the game again when Reinhart scored with 4:27 left in the second to make it 2-2.
Watson gave the Senators a 1-0 lead when he corralled a loose puck in front and slid it under Knight's pads at 4:38 of the first.
Huberdeau's goal tied the score 1-all after he skated in and fired the puck past Forsberg from in front with 6:55 left in the first.
For the first time in 647 days, "O Canada" was played pregame at the Panthers' home rink. Ottawa's visit was the first by a Canadian team since the Montreal Canadiens played at Florida on March 7, 2020. The Panthers' first game in Canada this season is at Calgary on Jan. 18; that'll be Florida's first game on Canadian soil since August 2020.
NOTES: Panthers F Anthony Duclair returned after missing the last eight games with a lower-body injury. ... F Aleksi Heponiemi was recalled from Charlotte (AHL). ... F Ryan Lomberg was placed in the NHL's COVID-19 protocol on Tuesday morning. ... D Gustav Forsling missed the game with a non-COVID-19 illness. ... Ottawa scoring first meant the Panthers have given up the first goal of a game 50% of the time this season, now 14 times in 28 games. ... Senators coach D.J. Smith has now coached against 40 different coaches at the NHL level after facing off with Panthers interim coach Andrew Brunette for the first time Tuesday.
Senators: Visit Tampa Bay on Thursday, the second of a three-game trip.
Panthers: Close a two-game homestand on Thursday against Los Angeles.