The bigger problem is the superstar center sustained a concussion that will keep him out of action for at least a little while longer.
After the game, Penguins coach Dan Bylsma announced that Crosby is expected to be out for a week.
"You don't want to see a guy go down like this, especially him, but we have to regroup and play better, that's it," said defenseman Kris Letang, the first of five Pittsburgh shooters stopped by Carey Price in the shootout.
Price, who made 31 saves through overtime, was perfect in the tiebreaker, turning aside Letang, Pascal Dupuis, Evgeni Malkin and Mark Letestu before denying Chris Kunitz on Pittsburgh's final attempt.
Pouliot deked Brent Johnson and let the puck slide into the right side of the net to give Montreal a win in its first shootout of the season.
"It's definitely a move where you really have to make the goaltender bite," said Price, who has seen Pouliot try it in practice. "You really have to get him to give up his edges or else it's not much of a move, but he did a good job of making him drop his right knee.
"As soon as you give up your right edge, then you're sliding that way. Your momentum is carrying you, and you can't stop it."
Pouliot also scored the tying goal in the second period as the Canadiens improved to 2-0-1 following a three-game losing streak.
Arron Asham scored in the first period for Pittsburgh, 1-2-1 in its last four games. Johnson made 22 saves, including stopping the only shot he faced in overtime.
"I think we played well in certain aspects of the game but we didn't manage the puck well," Letang said. "We turned the puck over in the neutral zone and that's what killed us because we could have kept that 1-0 lead the whole game."
It didn't help that they were missing Crosby, who leads the NHL with 32 goals and 66 points.
"We play 40 minutes a game without Sid on the ice so we're comfortable with knowing how we need to play and how it's going to be," Bylsma said. "We're going to keep playing exactly that same way and figuring out ways to win hockey games."
Crosby flew back to Pittsburgh on Thursday to be re-evaluated by team doctors after he was injured Wednesday in the Penguins' 8-1 home victory over the Tampa Bay Lightning.
"We wouldn't have thought he was OK to play," Bylsma said when asked if Crosby displayed any symptoms before Wednesday night's game after being hit in the Winter Classic last weekend. "He certainly saw doctors."
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Penguins forward Matt Cooke also returned to Pittsburgh because of personal reasons.
The Canadiens announced before the game that defenseman Josh Gorges will have surgery on his right knee and miss the rest of the season. Montreal is already without star defenseman Andrei Markov for the season because of a knee injury.
Montreal managed just one shot during a lengthy two-man advantage midway through the third. Pittsburgh was called for two straight delay-of-game penalties when Johnson and Paul Martin each cleared the puck over the glass while Alex Goligoski served a hooking penalty.
Penguins center Maxime Talbot beat out David Desharnais on a faceoff in Montreal's zone to set up the opening goal 2:14 in. Asham put away a rebound of Ben Lovejoy's slap shot for his fifth goal after the Pittsburgh defenseman one-timed Goligoski's pass back to the point.
Desharnais got his first point in two games since being recalled from Hamilton of the AHL on Friday when he assisted on Pouliot's goal 12:28 into the second. The diminutive center flipped a pass from behind the net to Mathieu Darche, who gloved the puck but was unable to get a shot away.
Letestu's clearing attempt went right to Pouliot, who snapped a shot over Johnson's left arm for his eighth goal.
"We wanted that goal back and we got it," Desharnais said.
Malkin missed an opportunity to give Pittsburgh a two-goal lead earlier in the second. The Russian center lost control of the puck when he went to his forehand on a breakaway, right after Montreal defenseman Jaroslav Spacek drove a shot off the right post.
- Crosby had recorded only one point -- an assist against the Lightning -- in three games since a 25-game point streak.
- Desharnais had one assist in six games with Montreal last season.
- Gorges had one goal and six assists in 36 games this season.