The Islanders have a chance to tie the Canadiens in the East when the teams continue their season series Saturday.
New York (30-23-8) has gained points in 13 of its last 15 games (9-2-4) and has 68 overall, trailing seventh-place Montreal (32-25-6) by two points and eighth-place Carolina by one. The Hurricanes play at Atlanta on Saturday night.
The Canadiens, meanwhile, have been able to hold off the Islanders by winning three straight after a six-game losing streak.
"You look at the standings, and every game we play is important," Islanders center Randy Robitaille said. "We're not looking during the game, but I can guarantee you that afterward, the guys are checking other scores to see how the race is shaping up."
A 3-2 shootout win over Toronto on Thursday night gave New York a 3-0-1 record on its seven-game homestand, which concludes with matchups against Philadelphia and St. Louis next week.
After rallying from a two-goal deficit Thursday, Robitaille capped the comeback by scoring the only goal of the shootout. The Maple Leafs missed all three of their shootout chances against Rick DiPietro, who made 27 saves.
DiPietro is 5-2-2 with a 1.94 goals-against average and one shutout in his last nine games.
"Ever since the All-Star break, we've been playing with a lot of confidence," DiPietro said. "We don't want to be in the position where we have to come back, but we're not afraid of it if it happens."
Trent Hunter scored twice in regulation for the Islanders on Thursday. His only other two-goal game this season was in New York's 4-2 win at Montreal on Feb. 3 in the teams' last matchup.
Saku Koivu had two goals and an assist for Montreal in its only other meeting with New York, a 4-2 Canadiens road win on Dec. 7.
Koivu's shootout goal provided the difference in Montreal's 6-5 win over Nashville on Tuesday night. The Canadiens fell behind by two goals less than four minutes into the game, and trailed by that margin two other times.
"Sometimes you need games like this to build the confidence," said Koivu, who has a goal and six assists in his last three games. "Hopefully, from here on, it will be a little easier to win games."
Montreal's winning streak has coincided with goaltender Jaroslav Halak's first three starts since being called up to replace All-Star Cristobal Huet, who had surgery on his left hamstring last week and is out indefinitely. Halak has a 3.26 GAA for the Canadiens after going 16-11-0 with an AHL-best 2.00 GAA and six shutouts in 28 games for Hamilton.
Sergei Samsonov, Michael Ryder, Mark Streit, Garth Murray and Alexander Perezhogin scored for Montreal on Tuesday.
Ryder scored for the fourth time in three games, tying Sheldon Souray for the team lead with 20 goals.
The Canadiens have scored seven power-play goals in their last three games, their best stretch since tallying eight over three games from Dec. 14-19.