Saku Koivu had a goal and two assists and Glen Metropolit also scored for Montreal, which ended a five-game winless streak. Tanguay and Andrei Markov had three assists. Carey Price made 22 saves for the Canadiens.
Montreal moved two points ahead of idle Florida into sole possession of the eighth and final playoff spot in the NHL East with each team having nine games remaining.
Ilya Kovalchuk and Joey Crabb scored for the Thrashers, who have lost three of their last four games. Atlanta's Kari Lehtonen allowed six goals on 22 shots.
Pregnant Mila Kunis wins 'Best Villain' at MTV Movie Awards
Pistorius testifies he didn't consciously pull trigger when he shot girlfriend