Mark Streit and Tomas Plekanec also scored for the Canadiens (28-18-5), who overcame a lacklustre 4-1 loss to the Maple Leafs in Toronto on Saturday to win for only the fifth time in their last 12 games.
Chris Phillips scored the lone goal for the Senators (29-21-2), who lost for only the second time in nine games.
The game was played after a 48-minute ceremony to retire the jersey of Ken Dryden, and after a slow start to the game the Canadiens gave their former goaltender something to cheer about.
David Aebischer made 26 saves for the Canadiens, none bigger than a flashy glove grab on Jason Spezza 11:02 into the third period to maintain Montreal's two-goal lead.
Ray Emery made 25 saves in his eighth straight start for the Senators.
The win moved Montreal past Ottawa into fourth place in the Eastern Conference with 61 points, one point ahead of the Senators and three ahead of the Carolina Hurricanes. The Canadiens have a game in hand on both the Senators and the Hurricanes.
Trailing 1-0 midway through the second period, the Canadiens exploded for three goals in a span of 2:24 to take a 3-1 lead.
The Canadiens took advantage of a hooking penalty to Chris Neil when Souray scored his 14th power-play goal of the year off a one-time blast from the point at 10:55, just moments after Emery stoned Montreal's Alex Kovalev from in tight.
Streit made it 2-1 at 12:01 when Andrei Markov sent him in alone with a brilliant breakaway pass and he deked Emery between the legs for his fourth of the season.
Souray took a high-sticking penalty behind the play in his own end just 31 seconds after the Streit goal, but it was the Canadiens who capitalized while a man down to score their league-leading 13th shorthanded goal of the year.
Wade Redden had trouble handling a Canadiens clearing attempt at the blue-line and Plekanec pounced on the bouncing puck, held off Tom Preissing to go in alone on Emery and put a backhand top corner for his 10th goal of the season at 13:19.
Phillips gave Ottawa a 1-0 lead, lofting a soft wrist shot from the blue-line that made it through a crowd and past Aebischer at 0:52 on Ottawa's first shot of the game.
It was the third time this season the Senators scored within the first minute of a period.
Notes: Senators D Anton Volchenkov played in his 200th career NHL game ... Canadiens winger Alexander Perezhogin was a healthy scratch for the second time in eight games. Perezhogin has one goal and one assist in his last 22 games played ... Canadiens C Radek Bonk's wife gave birth Sunday to the couple's second child, a girl named Kennedy ... The loss dropped the Senators record in Monday games to 0-2-2. It is the only day of the week
where the Senators are winless this season.