Filip Gustavsson stopped 36 shots in the Senators (19-27-5) net while Tim Stützle and Thomas Chabot had goals. Cayden Primeau made 21 saves while Jeff Petry and Tyler Toffoli scored in regulation for the Canadiens (23-18-9) before Cole Caufield won the game in overtime.
"For two periods we played okay and obviously in the third period didn't manage the puck at all," Sens head coach D.J. Smith said. "We just kept giving it away and changing and didn't make plays. That's not our game."
Caufield ended the game at 2:25 of the extra frame as he snuck in back door and buried Petry's cross-ice pass for his first career NHL goal and the additional point.
"Just a lot of mistakes in the third period," Smith said. "There wasn't one particular thing. There was a lot of mistakes. [We were] just careless with the puck. It was a lot of things we haven't done in a long time [that] crept in tonight against a desperate team."
Ottawa clanged the crossbar twice inside the opening 5:30 as both Connor Brown, and then Josh Brown, came within inches of giving Ottawa an early lead.
Stützle broke the deadlock with 5:08 left in the second as from the high slot he let a wrister go that flew past Primeau as the rookie buried his ninth of the season.
Chabot doubled the lead at 5:51 of the third period as he found himself wide open in the slot off of a lovely Evgenii Dadonov backhand pass as the Sens d-man scored his sixth goal of the campaign.
Petry got Montreal on the board at 8:12 as he patiently waited for a seam to open before scoring his 12th goal from the slot past Gustavsson's blocker. Nick Suzuki thought he had tied the game on the power play at 10:37 but the goal was waved off after a review for goaltender interference.
Montreal did get the equalizer with 5:35 left as on the man advantage, Toffoli ripped a one-timer for his 27th of the season to make it 2-2 from inside the left circle.
"We're killing a penalty because we don't put the puck in and we turn it over," Smith said. "The game rewards the better team most of the time and in the third period they earned it."
Josh Norris had his first NHL fight in the second period as he dropped the mitts with Montreal defenceman Alexander Romanov.
With his goal, Chabot tallied the 150th point of his career and sits fourth all-time in franchise history for points by a blueliner.
"We're going into the third with the lead and you've got to learn to close out teams and obviously those games sting," Chabot said. "You want to win, you want to get job done but those are learning things that we've got to make sure when we get in that situation again, we're getting it done."
Tonight's loss officially eliminated the Senators from playoff contention.
Ottawa is back in action Monday when they host Winnipeg at Canadian Tire Centre.
