Phillip Danault and Brendan Gallagher both collected assists on the play to extend their respective point streaks to five straight games.
Unfortunately, Brady Tkachuk responded for the Senators with a power play goal just four minutes later.
That cut the Canadiens' lead to 2-1.
Then, Connor Brown tied things up for Ottawa with 6:55 remaining in regulation.
That capped the scoring through 60 minutes, so overtime was required.
Defenseman Ben Chiarot scored the game-winning goal in the extra frame.
The Habs will be back in action on Saturday night when they play host to the Detroit Red Wings at the Bell Centre.