Tim Stutzle also beat Montreal goalie Carey Price in the shootout. Ottawa's Brady Tkachuk opened with a miss and Senators netminder Matt Murray stopped Corey Perry and Jonathan Drouin.
It capped a wild and entertaining game between the rivals.
Both teams had excellent chances in overtime. Stutzle had two glorious opportunities but couldn't convert, and Montreal's Tyler Toffoli was stoned on a breakaway with about a minute to go.
It looked like Montreal's Brendan Gallagher had scored with 2.1 seconds left in regulation, but the goal was waved off after a review due to goaltender interference.
Tkachuk had two goals for Ottawa, with Drake Batherson and Erik Brannstrom also scoring. Shea Weber had two goals for Montreal. Drouin and Toffoli had a goal apiece.
Tkachuk also chipped a couple of teeth when he was high sticked and got in a fight with Ben Chariot.
''It's got to be one of the crazier games to have been a part of,'' Tkachuk said. ''It was just a lot going on. I'm excited about how I'm going to feel tomorrow morning.''
After a slow start, the last-place Senators have picked up their play of late. Ottawa entered with three wins over its last five games, including a 3-2 overtime victory over the Habs last Sunday.
Senators coach D.J. Smith said his team was ''dangerous'' in both games.
''We've got a different hunger and a different attack mentality,'' he said. ''When you get a couple on the power play and your penalty kill is good, you usually get points in the NHL.''
The 9-5-4 Canadiens, meanwhile, were 5-1-2 last month but entered with just one win in their last five games to drop them into fourth place in the North Division.
''It's steps at this point,'' Weber said. ''We're trying to get out of this and we're going to get out of it together.''
Ottawa will continue its five-game homestand on Thursday against Calgary. It will be the first of three straight games against the Flames.
Montreal visits Winnipeg on Thursday. The Jets will also host the Canadiens on Saturday.
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