Florida outshot Ottawa 26-4 in the first period.
"The first period, it's our worst period of the year for sure," Senators coach D.J. Smith said. "Just weren't ready when the game started. We battled back and we gave up a goal at the end of the second period, and then we give up a goal with three minutes to go. I mean, we kept battling but we've got to be better than that."
Shane Pinto scored 37 seconds of the second period to cut it to 2-1, one-timing a pass from Claude Giroux on the power play. It was Pinto's sixth goal in the past seven games.
Brady Tkachuk tied it 2-2 at 3:23 with a shot from the left face-off dot.
Ottawa appeared to take a 3-2 lead at 5:26 of the second, but Tim Stutzle's goal was overturned after Florida coach Paul Maurice challenged the play for goaltender interference.
Verhaeghe then put Florida ahead 3-2 at 19:23 of the second when he one-timed Montour's pass at the top of the right circle.
After Montour scored the go-ahead goal, Tkachuk shot into an empty net with 14 seconds remaining for the 5-3 final.
"It was a good win," Maurice said. "They had won four of the past five coming in, and are a quick strike team. They are a team that has some high-end skill with some talented young players, and if they catch you in open ice, they're going to finish."
NOTES: Senators forward Alex DeBrincat had his six-game point streak end. … Florida set a team record with 58 shots on goal.