Markov, Mathieu Dandenault and Michael Ryder had the goals in regulation for Montreal, which won its fourth consecutive game.
Evgeni Malkin had three assists for the Penguins, who got a Ryan Whitney goal with 1:52 to play in regulation to earn a point.
After 15 shooters in the shootout could not score on either Montreal goalie Carey Price or the Penguins' Dany Sabourin, Markov made a move and beat Sabourin between his legs.
Whitney also went 5-hole against Price off a pass from Malkin to tie the game late. The Penguins were playing 6-on-4 due to a power play and the pulling of Sabourin, the team's backup who was only in after starter Marc-Andre Fleury was ineffective.
Dandenault scored the game's first goal at 7:13 of the opening period on a slap shot that Fleury, and the Canadiens took a 2-0 lead 3½ minutes later when Markov scored on a power play. Saku Koivu's shot from the point was deflected in front of the net by Christopher Higgins, and Markov picked up a loose puck and backhanded it past Fleury.
Forty-nine seconds into the second period, Fleury's night was over. Ryder beat him high on the glove side on a clean wrist shot from just above the right faceoff circle. Fleury, who allowed three goals on 15 shots, was lifted by Penguins coach Michel Therrien.
One minute after Ryder's goal, Montreal's Alexei Kovalev took a boarding penalty for checking Malkin from behind. Sidney Crosby reacted by lunging at him and tackling him to the ground. That resulted in coincidental roughing minors for Crosby and Kovalev, an ex-Penguin.
Watching their young captain defend his teammate seemed to spark Pittsburgh, which scored twice in the next seven minutes.
The Penguins, who have scored a power play goal in every game this season, cut the deficit to 3-1 when Petr Sykora corralled a pass out of midair from Malkin while on the power play at 3:03 of the second. He then beat Price to the short side.
Crosby scored his fourth of the season with 11:44 to play in the second on a 3-on-2 with Malkin and Ryan Whitney.
But Price and the Montreal defence shut down Pittsburgh in the third period until the team played almost the entire final four minutes while on the power play, resulting in Whitney's goal.
Notes: The Canadiens' Markov, Dandenault, Koivu, and D Michael Komisarek each have three-game point streaks. D Roman Hamerlik has a four-game streak. ... The Canadiens have outscored opponents 14-5 in the first period of games this season. ... Price was making his third career start. He beat the Penguins at Mellon Arena in his NHL debut Oct. 10. ... After being shut out in the season opener, Crosby has at least one point in all nine games since.