Koslov scored his 10th goal this season to put Atlanta ahead 1-0 at 4:31 of the first period.
Eric Perrin's seventh late in the second gave Atlanta a 2-1 lead.
Keri Lehtonen stopped 37 of 39 shots for the Thrashers, who have won three games in a row.
Montreal's goals were scored by Siarhei Kastsitsyn in the first and Alexei Kovalev in the third, with Kovalev's 15th goal this season creating a 2-2 tie with just under 12 minutes left in regulation.
Christobal Huet stopped 26 of 28 shots for the Canadiens, who had won three of their previous four games.
On the power play, Atlanta went 1 for 4 while the Canadiens did not convert on either of their man-advantage opportunities.