Mike Fisher scored the game-winner with 1:27 left in the extra session, taking a long pass from Erik Karlsson and streaking toward the Montreal goal before lifting a backhand shot past netminder Jaroslav Halak.
Fisher's goal was his team leading fifth game-winner and 19th tally of the season.
"It always feels great to score the overtime winner," Fisher told reporters. "It was a great play by Karlsson. I just tried to get some speed, threw it at the net and somehow it went in."
The win widened second-place Ottawa's advantage over third-placed Montreal in the Northeast division to 10 points.
While the Senators have soared to fifth place in the Eastern Conference on 66 points the Canadiens have struggled, losing six of their last eight including a January 16 meeting with Ottawa when they were tied with 50 points.
However, the Senators did receive some bad news. Winger Nick Foligno broke his right leg late in the third, blocking a shot by Montreal defenseman Marc-Andre Bergeron, and would miss six to eight weeks, the team said.
Brian Gionta forced overtime by netting Montreal's second power-play goal of the game with 2:45 remaining, converting a pass at the top of the crease from Andrei Markov.
The Senators opened a 2-0 lead on a first period goal by Alex Kovalev and a score by Jason Spezza midway through the second before Benoit Pouliot replied for Montreal later in the period.
Ottawa netminder Brian Elliot made 27 saves for his seventh consecutive win and 17th of the season. Halak stopped 34 of 37 shots in the loss.
(Reporting by Mike Mouat in Windsor, Ontario; Editing by John O'Brien)