Andrei Markov shot a puck off the glass from his own end that came bouncing into the Thrashers zone towards defenceman Andy Sutton. When he fanned on the puck, Perezhogin swept in and beat Hedberg with a one-handed shot for his second of the year and a 2-1 lead at 6:46 of the third.
The goal was Perezhogin's first in nine games.
Michael Ryder and Radek Bonk also scored for the Canadiens (11-5-3), who have yet to lose consecutive games this season and won their third in their last four.
Glen Metropolit scored for the slumping Thrashers (12-7-3) in their first of a three-game road swing.
Cristobal Huet was solid in the Montreal net with 39 saves to win his third straight start and run his record to 6-2-2. Huet has allowed two or fewer goals
in five of his last six starts after a shaky start to the season.
Johan Hedberg started in place of the suddenly struggling Kari Lehtonen, who has allowed 13 goals on 68 shots in his last three starts. Hedberg made 30 saves, and was particularly sharp on a spectacular glove save on Sergei Samsonov late in the first and breakaway saves on both Bonk and Ryder in the third.
Ryder gave the Canadiens a 1-0 lead at 14:18 on a power play to snap a nine-game goalless drought.
Sheldon Souray blasted a shot from the point that was blocked by Sutton, but the puck bounced right to Ryder in the slot who roofed a slap shot over Hebderg's right shoulder for his fifth goal of the season.
The Canadiens nearly went ahead 2-0 late in the second when Samsonov's shot at a wide open net was caught by Hedberg on the goal-line. The play went trough a lengthy video review before the save was confirmed.
After a second period with few chances and little flow, the Thrashers tied the game 1-1 at 3:30 of the third when Metropolit's seemingly harmless shot bounced off Souray and past Huet for his third goal of the season.
After Perezhogin gave Montreal the lead, Bonk added an empty-netter at 18:46 of the third for his fourth of the season.
Notes: Canadiens Hall of Fame defenceman Serge Savard had his No. 18 jersey retired in a pre-game ceremony.