Jacob Fowler made 25 saves for his seventh straight win, Chris Kreider had a goal and an assist, and Lane Hutson had two assists for Montreal (9-3-2), which extended its point streak to seven games (6-0-1).
Sidney Crosby scored with 3:11 remaining in the third period to draw the Penguins within 5-4 and tie Marcel Dionne for sixth on the NHL points list with 1,771.
Crosby added two assists, Erik Karlsson also had a goal and two assists, and Rickard Rakell and Tommy Novak each had a goal and an assist for Pittsburgh (5-7-2), which was 2-0-1 in its previous three games. Sergei Murashov made 22 saves.
Karlsson’s power-play goal at 2:08 of the first period put Pittsburgh ahead 1-0. Crosby became the NHL’s all-time assist leader with one team when he set up Karlsson, who scored on a one-timer from the left point.
Crosby’s 1,112th assist, all with the Penguins, moved him one ahead of Ray Bourque, who had the first 1,111 of his 1,169 career assists with the Boston Bruins.
Oliver Kapanen tied it 1-1 at 2:41 with his first goal of the season, scoring with a one-timer past Murashov’s blocker from the left face-off circle.
Anderson put Montreal up 2-1 at 3:05, just 24 seconds after Kapanen tied it. He curled toward the right face-off dot after the puck came to him when Pittsburgh forward Hendrix Lapierre’s pass went off Kreider and shot past Murashov to the blocker side for the third goal in 57 seconds.
Novak tied it 2-2 at 7:28. He cut across the goalmouth and slid the puck between Fowler’s pads on the backhand.
It appeared Montreal’s Cole Caufield scored a fifth goal in the first 9:26, but it was overturned after Pittsburgh challenged for goaltender interference.
Alexandre Texier did make it 3-2 for the Canadiens at 1:54 of the second period. Hutson spun around and sent a pass to the right edge of the crease to set up Texier, who deked around Murashov’s pad to score.
Kreider pushed it to 4-2 at 2:21. Murashov made a pad save on his initial shot, but Kreider stuck with it and scored with a backhand off the rebound.
Rakell drew Pittsburgh within 4-3 at 3:45 with the third goal in 1:51. He scored from the right side of the slot off a pass from Karlsson, who cut off Montreal defenseman Arber Xhekaj’s clearing attempt right on the blue line to set up the goal.
Anderson made it 5-3 at 13:06. He got credit for his second goal of the game when the rebound of Hutson’s shot off Murashov’s left pad struck him before going into the net off Penguins defenseman Kris Letang’s left leg.
Crosby cut it to 5-4 at 16:49 of the third when he scored a power-play goal from the right edge of the crease.