Jason Spezza also scored three points for Ottawa, but left in the second with an upper-body injury.
Crosby's 30th goal spoiled Brian Elliott's shutout bid.
But Crosby, the NHL's leading scorer with 61 points, also conceded a couple of costly penalties.
Mike Fisher scored the first of Ottawa's two power-play goals midway through the first after Crosby was sent off for hooking. Karlsson made it 2-0 at 13:42 during a delayed slashing call against Crosby, who also hooked Chris Phillips late in the second to negate a Penguins power play.
Elliott turned aside 44 shots, including 22 in the second period, as Ottawa won consecutive games for the first time since a season-high four-game winning streak in early November.
Marc-Andre Fleury made 21 saves for Pittsburgh, which had won 16 of 18, including three in a row.
In Raleigh, North Carolina, Alex Ovechkin ended an eight-game drought without a goal and added an assist for Washington, which held on for the win.
Mathieu Perreault and David Steckel also scored for the Capitals. They have won three of four and swept the Hurricanes on their home ice for the first time since the 1997-98 season.
Tuomo Ruutu and Jussi Jokinen each had a goal and an assist, and Cam Ward made 27 saves for the Hurricanes.
Carolina has lost three straight in regulation for the first time this season.
In Chicago, Patrick Sharp scored two goals and Marty Turco made 26 saves to lead the Blackhawks to their fourth straight win.
Turco lost a bid for his second shutout this season when Derick Brassard scored on a screened power-play goal with 2:26 left in the third period.
Tomas Kopecky and Dave Bolland also scored for Chicago, which has allowed just five goals during its winning streak.
Star forward Marian Hossa returned after missing 10 games with a lower body injury and assisted on Chicago's first two goals.
In Atlanta, Vincent Lecavalier's second goal of the game - a power-play 1:13 into overtime - gave Tampa Bay victory.
Steven Stamkos also scored his 28th goal for the Lightning, who have won two straight and six of seven.
Lecavalier has six goals this season and three in two games.
Zach Bogosian and Fredrik Modin scored for the Thrashers.
Ondrej Pavelec made 31 saves.
The Lightning have won nine straight against Atlanta, including four this season over their Southeast Division rival.
In St. Paul, Minnesota, Henrik Zetterberg scored a goal and an assist to power the Red Wings to victory.
Daniel Cleary, Kris Draper and Tomas Holmstrom also scored for Detroit, which won for just the second time in five games.
Brent Burns had a late power-play goal for Minnesota, which lost for the first time in four games.
In Dallas, Jason LaBarbera stopped 29 shots for his fifth career shutout and Kyle Turris scored in the second period, leading Phoenix to the win.
LaBarbera was making his fifth straight start in place of Coyotes No. 1 goalie Ilya Bryzgalov, who is out because of a lower-body injury.
The goaltender, who had surrendered 15 goals over his previous four starts, turned aside a penalty shot by Loui Eriksson in the second period.
The Stars pulled goalie Kari Lehtonen for an extra attacker with 1:32 left, but Eriksson missed the net on a close-range attempt.
In St. Louis, Jaroslav Halak made 32 saves for his fourth shutout and David Backes scored twice, sending St. Louis to its third consecutive win.
Halak, who came to the Blues in an offseason trade with Montreal, has been in goal for each game during the winning streak. Sunday's shutout was the 13th of his career.
Pekka Rinne stopped 24 shots for Nashville, which has lost four straight. The Predators have scored just three goals during the slide.
In Newark, New Jersey, Jonas Gustavsson stopped 29 shots, Colby Armstrong scored two goals and Toronto ended a three-game losing streak.
The Devils (9-24-2), who have the fewest points in the NHL, have lost five straight and 10 of 11 this month. New Jersey is 0-2 since Jacques Lemaire replaced John MacLean and began his third stint as Devils coach.
John Mitchell and Nikolai Kulemin also scored for the Maple Leafs, who are 10 points ahead of the last-place Devils.
In Uniondale, New York, Dwayne Roloson stopped 37 shots, and the Islanders stretched their winning streak to three.
Blake Comeau, Michael Grabner, P.A. Parenteau and James Wisniewski scored for the Islanders, who tied their longest winning streak of the season and extended their point streak to five games (4-0-1).
New York (9-18-6) moved four points ahead of New Jersey, which has the fewest points in the NHL.
The announced attendance was only 3,136 on a snowy night on Long Island. Newsday reported on its website that the NHL turned down the requests of the Islanders and Nassau County to postpone the game.
Tomas Plekanec scored Montreal's only goal. Carey Price made 21 saves.
In Los Angeles, Dustin Brown scored a goal and an assist after getting flattened by a punch, as the Kings beat the Ducks in the second installment of the “Freeway Faceoff.” Wayne Simmonds, Anze Kopitar and Justin Williams also scored against Jonas Hiller, who stopped 19 of 23 shots. He was replaced with 2:03 left in the second period by Curtis McElhinney after Brown's power-play goal made it 4-1.
Matt Beleskey, playing his first game with the Ducks since Dec. 7 after being recalled from Syracuse of the AHL, scored Anaheim's goal. In the first period, he sent Brown to the ice with an uppercut to the face after the Kings captain got a little too close to Hiller as he froze the puck in the crease.
In Vancouver, Kevin Bieksa's goal with 24 seconds left gave the Canucks the victory.
Alex Burrows sent a long pass from behind the net to the point where Bieksa fired it past screened goalie Nikolai Khabibulin.
The Canucks earned their 11th win in 14 games. They have not lost in regulation since Dec. 5 against St. Louis. Jeff Tambellini and Mikael Samuelsson also scored for Vancouver.
Ryan O'Marra netted his first NHL goal, and Ryan Whitney also scored for the Oilers, who are winless in three meetings with Vancouver this season.
