The Penguins won for the eighth time in nine games, building a 4-0 lead through two periods. The Canadiens had a four-game winning streak snapped.
Crosby scored the only goal of the first period, and then opened the second with a backhander that eluded Jaroslav Halak. The Pittsburgh superstar scored his third goal on a wraparound with 4:27 left in the second period, driving Halak from the game.
Halak allowed four goals on 23 shots. Carey Price gave up two goals on 14 shots in relief.
The win went to Marc-Andre Fleury, who made 23 saves. Fleury lost his bid for a shutout 5:39 into the third on a power-play goal by Tomas Plekanec.
Crosby, who took nine shots, boosted his goal total for the season to nine. It was his first hat trick of the season and this was the fifth game out of 12 in which he has scored a goal.