"You get an idea in your head what you're going to do," Koivu said. "I was nervous because I knew if I didn't score, the game was done. Lucky enough, I was able to get the tying goal there."
Halak, who had 37 saves in the game, forced Yanic Perreault wide on the Maple Leafs' third shot before Kostitsyn used a move similar to Koivu's as he deked Andrew Raycroft before putting a forehand into an open left side for the deciding goal.
"My move was my favorite move," Kostitsyn said. "I saw Saku do it before and knew I could do the same motion and score."
The sellout crowd of 21,273 erupted into cheers when Halak followed with a stop on Darcy Tucker as the win drew Montreal even with Toronto at 78 points in the crowded race for the final two playoff spots in the Eastern Conference.
"If we had lost this game it would have been real tough to get back in the race," Koivu said. "Now, we're tied. That extra point was big for us. The situation for both teams from here on until the end is every game is a playoff game and a must-win. We'll battle for the next two weeks and see where that takes us."
It was the fourth shootout in seven games this season between the Northeast Division rivals.
"We showed a lot of character to get back in the game and even though we were down pretty much the whole game, we got a point," Sundin said.
Pavel Kubina tied the score at 2 with his sixth goal 8:41 into the third. The Toronto defenseman beat Halak with a wrist shot inside the right post from high in the slot after he received a backhand pass from Kyle Wellwood.
"We came here to get two points but we battled hard all 65 minutes and we had some quality chances," Kubina said. "They were a little bit more lucky in the shootout. They got two and we got one."
Kostitsyn scored his first NHL goal in more than 14 months when he put Montreal up 1-0 at 6:05 of the first period. After taking a pass from Christopher Higgins, Kostitsyn carried the puck into the Maple Leafs' zone before putting a low shot between defenseman Hal Gill's legs and past Raycroft inside the right post. It was his first goal with the Canadiens since Jan. 5, 2006.
Wellwood, who didn't play in Friday night's 5-1 loss at Washington, tied it with his 10th goal, on the power play, at 15:01.
"(Friday) night was a bit of a disaster all around," said Raycroft, who stopped 29 shots. "We didn't play well enough to deserve to get two points. Tonight, it was one of those ones where we both played back to back and slugged it out and put pucks at the net, going off skates and hitting posts."
Koivu scored his 19th goal midway through the second to put the Canadiens back ahead and reach 60 points for the third time in his career.
Halak, winner of three straight starts from Feb. 18-22 to begin his career, started in place of David Aebischer, who had started three in a row and allowed three third-period goals in Friday's 6-3 loss at Pittsburgh.
The Slovak rookie evened his record at 4-4 in his first start since March 8, when he allowed five goals before he was pulled in the second period of a 6-2 loss at Atlanta.
- Referee Dan Marouelli replaced Kevin Pollock, who was originally scheduled to work the game before overnight snow in the Montreal area wreaked havoc with travel plans.
- It was the 681st regular season game between the NHL's two oldest franchises. Montreal has a 322-271 margin in wins, including games won in overtime and shootouts. The teams tied 88 times.
- Tucker fought in the first with Canadiens defenseman Francis Bouillon, who had knocked the Maple Leafs center to the ice with a punch earlier this season. Tucker had several stitches around -- even inside -- his right nostril after he was cut by a stray stick later in the opening period. There was no penalty on the play, which happened in front of Montreal's net while Bouillon checked Sundin heavily into the boards.
- Kostitsyn has six assists in 13 games with Montreal this season, including three in a 5-3 win over the New York Islanders on Tuesday for his first three-point game. He had two goals in 12 games with Montreal last season.
- Koivu has had at least 60 points three times, including 62 last season. He had a career high 71 points in 2002-03, his first full season after battling non-Hodgkin intra-abdominal lymphoma.