Kostitsyn and Saku Koivu scored in the shootout for Montreal, while the Thrashers came up empty in two chances against Cristobal Huet. Slava Kozlov shot wide and Marian Hossa’s attempt to go five-hole was blocked by Huet.
Michael Ryder also scored for the Canadiens in regulation, and Hossa and Pascal Dupuis had the Atlanta goals.
It was the third straight shootout between the teams, the previous game also going to extra time tied at 2.
Atlanta won the first two, but Montreal got the Thrashers in this one for its fourth win in five games.
Montreal tied the game at 1 on a masterful goal by Kostitsyn at 5:24 of the second. The 20-year-old Russian took a pass near center ice, cut to his left to avoid Eric Perrin, shifted back to his right to get around defenseman Ken Klee and flipped a shot past Kari Lehtonen for his 12th of the season.
Michael Ryder gave the Canadiens their first lead with 13:58 left in the third, finishing off a nifty bit of passing.
Skating along the boards, Bryan Smolinski worked the puck over to Guillaume Latendresse, who relayed it to Ryder cutting in front. He jabbed at it with his stick, managing to flip a wobbly shot over Lehtonen’s left shoulder.
But the Thrashers tied it up with a gift from Huet.
As a Montreal power play was ending, the goalie ventured into the corner to play the puck. Huet froze when trying to decide whether to dump the puck to teammate Roman Hamrlik or clear it out of zone.
Perrin sneaked in to poke the puck away, and it skidded right in front of the unguarded net to Dupuis. He buried it for his ninth goal with 10:58 left in regulation.
The Thrashers jumped ahead 1-0 late in the first when Hossa, with what looked like an attempted pass across the crease, instead struck Huet in the arm.
The puck wound up behind the goalie, giving Hossa his 20th goal.Notes: Atlanta D Tobias Enstrom took a hard hit behind the net from Sergei Kostitsyn, knocking off his helmet. Enstrom skated slowly to the locker room, but returned to the game after getting checked out. ... Montreal improved to 7-5 in shootouts.
, while the Thrashers dropped to 5-3.