Carey Price, who made 31 saves through overtime, was unpassable in the shootout. He denied four Penguins before stopping Chris Kunitz on Pittsburgh's final attempt.
Pouliot deked Brent Johnson and let the puck slide into the right side of the net as Montreal won in its first shootout of the season. He also scored the tying goal in the second period.
Arron Asham scored in the first period for Pittsburgh.
Crosby, who leads the NHL with 32 goals and 66 points, missed his first game of the season because of an undisclosed upper body injury.
In Denver, back-up goalie Jason LaBarbera made 34 saves for his second shutout in three starts as Phoenix beat Colorado.
The Coyotes were without goalie Ilya Bryzgalov, who missed the game because of a family medical issue. LaBarbera filled in and clamped down on the NHL's fourth-highest scoring team.
Taylor Pyatt scored both Phoenix goals, the second an empty-netter.
In Los Angeles, Nashville fought back to beat Los Angeles and notch a fourth straight win.
Patric Hornqvist scored two goals, Colin Wilson and Sergei Kostitsyn both had a goal and two assists, and Marek Svatos scored his first goal for the Predators.
Los Angeles slid to its season-worst fifth straight loss despite second-period goals to rookie Kyle Clifford and Jarret Stoll.
In San Jose, coach Lindy Ruff brought up his 500th career victory as Buffalo beat San Jose.
Ruff became the 16th NHL coach with 500 wins and joined Montreal's Toe Blake as the only ones in the club who got all their wins with one team.
Ruff reached the milestone in convincing fashion as Buffalo got goals from Luke Adam and Jochen Hecht in the first period and then stellar goaltending from Ryan Miller.
Thomas Vanek scored his team-leading 16th goal for the Sabres.
In Boston, Minnesota extended its record of never having lost at Boston.
Cal Clutterbuck scored the go-ahead goal on a giveaway from Marc Savard in the Bruins zone.
Martin Havlat also had a fluky goal for the Wild, converting four seconds into a power play.
Clutterbuck also assisted on Mikko Koivu's empty-netter with 43 seconds left.
The Bruins were 0 for 4 with a man advantage and have never scored a power-play goal against Minnesota.
Steven Kampfer scored for Boston.
In Toronto, the hosts bounced back from blowing a three-goal lead to defeat St. Louis in a shootout.
Tyler Bozak beat Ty Conklin with a wrist shot for the decisive score, but the highlight of the shootout was the move by teammate Mikhail Grabovski, who made a 360-degree turn while cutting across the top of the crease and tucked the puck into the net.
The Maple Leafs seemed to be in control when Phil Kessel's second goal of the game early in the third period made it 5-2.
But the Blues clawed back with a goal by Brad Winchester that was confirmed by video review. Eric Brewer's point shot found an opening to make it 5-4, and Matt D'Agostini completed the comeback when he was sent in alone and scored with a backhand deke.
Grabovski, Versteeg and Colby Armstrong had scored earlier for the Maple Leafs.
Alex Steen and David Backes had the other goals for St. Louis.
In Newark, New Jersey, Danny Briere and Scott Hartnell scored two goals apiece to lead Philadelphia over fast-fading New Jersey.
Ville Leino had a career-high three assists, and Brian Boucher made 18 saves as the Flyers improved their NHL-best road record to 13-4-3.
Briere snapped a 2-2 tie early in the third period with his 19th goal and gave the Flyers breathing room with 8:26 to go when his centering pass deflected past goalie Johan Hedberg.
Dainius Zubrus and David Clarkson scored for New Jersey, which has suffered 28 defeats in regulation already this season - one more than the Devils had in each of the previous two seasons.
In Edmonton, the hosts broke a seven-game losing streak with a victory over New York.
Dustin Penner had a short-handed goal and an assist, which Gilbert Brule also scored for the Oilers.
Edmonton scored both goals in the first 5:17 on only three shots against goalie Nathan Lawson, who was pulled after the second tally.
Blake Comeau had the lone goal for the Islanders (12-20-6), who fell three points behind the Oilers for 28th place in the standings.