Oilers rookie netminder Devan Dubnyk made 21 stops, and still remains in search of his first NHL win.
The victory, combined with a Philadelphia Flyers loss to Boston, puts both teams at 74 points. The Flyers hold the sixth spot in the Eastern Conference as they have three games at hand. Boston maintains the eight position with 72 points.
The first ten minutes of the period gave an indication of a wild night on the scoreboard.
"No game is easy this time of the year," Gionta said, citing that a win against a team just playing out the season is just as important as one against a playoff contender.
At 15:25 of the second period Kostitsyn and Dominic Moore assisted on Moen's eighth goal of the season. It was the big winger's first goal in 34 games, dating back to December 16, 2009.
The Moore line retook the lead for the Canadiens, at 8:05, when Kostitsyn worked his way out of the corner and ripped a wrist shot by Dubnyk, snapping his own eleven-game goal scoring slump.
"It's important to have production from different people," said coach Jacques Martin "Since the Olympics, they (the third and fourth lines) have raised their level of play, and they've contributed."
The Canadiens closed out the final period with the man advantage, when the Oilers were caught with seven skaters on the ice. The power play carried into the overtime, where Montreal managed just one shot and even managed to ice the puck. They closed out the night going 0 for 7 with the man advantage.
"We have to play better on the power play," Markov said. "We have to shoot more and stay in front of the net. Sometimes it was a bit fancy, but wehave to score."
Edmonton then had a brief but unsuccessful man advantage, to close out the extra time, when Tomas Plekanec slashed Horcoff.
Plekanec - five hole attempt stopped
Potulny - stopped
Gomez - five hole attempt stopped
Horcoff - stopped
Gionta - five hole attempt stopped
Brule - off Halak's glove and off the post
Pouliot - as CJAD's Murray Wilson said, "Someone change the record" five hole stopped
Nilsson - Had Halak beat but coudn't get puck in
Andrei Kostitsyn - Goal!
Gagner - stopped and 0 for 7 on shootouts
"It's all about luck in shootouts, it's all about 50/50," Halak said. "It was a great great win, even though I didn't play my best, but it happens."
The Canadiens close out their three-game homestand Saturday night when they host the Boston Bruins.
Three: 1. Sergei Kostitsyn 2. Shawn Horcoff 3. Andrei Markov