Elliott got his fifth career shutout as Ottawa won for just the second time since the Olympic break (2-7-1). The Senators also lost five in a row from Jan. 5 to 12 before putting together a franchise-record 11-game winning streak on their way to winning 13 of 15 prior to the break.
Peter Regin scored his first goal in 10 games midway through the first and Karlsson added a power-play goal in the third for Ottawa, which moved into sole possession of fifth place in the Eastern Conference, two ahead of Montreal and Philadelphia.
Jaroslav Halak stopped 26 shots in his eighth straight start for the Canadiens, who lost in regulation for the first time in eight games (6-1-1). Montreal ended its season-high six-game winning streak with a 3-2 shootout loss in Toronto on Saturday.
Canadiens left wing Travis Moen departed 10:41 into the second after he was cut on the face by Ottawa forward Matt Cullen's skate.
Moen, who does not wear a visor, was cut by the blade of Cullen's skate when the Senators veteran was upended along the boards in the left corner of Ottawa's zone. Moen was trailing blood as he was rushed off the ice with trainer Graham Rynbend.
A Canadiens spokesman said that Moen was not expected to go to a hospital for any further medical attention.
Regin gave Ottawa a 1-0 lead 10:15 in when he redirected Karlsson's pass at the edge of the crease for his 10th goal.
With Montreal's Dominic Moore off for hooking, Karlsson added some breathing room for the Senators when he picked up his second point of the game with his second goal of the season 8:17 into the third. The rookie defenseman drove a slap shot from the point through traffic and past Halak.
Notes
Canadian figure skater Joannie Rochette was on hand for the game. Rochette, who won an Olympic bronze medal in Vancouver after her mother died suddenly just prior to the competition, received a standing ovation from the Bell Centre crowd when she was introduced on the video board during the first period. … Senators LW Milan Michalek missed his second straight game because of a knee injury. … Elliott's last shutout was on Jan. 26 when he made 24 saves in a 3-0 win over Martin Brodeur and the New Jersey Devils. … The Canadiens have been shut out seven times this season.