Each club tries to earn precious points and avoid being eliminated from postseason contention when they meet on Thursday.
It's the final home game of the season for New York (37-30-12), which finishes up at Philadelphia and New Jersey. The playoff outlook is much more dire for the Islanders, who have 86 points, three behind the ninth-place Maple Leafs (39-30-11).
Both teams are chasing Montreal, which currently occupies the eighth and final spot with 90 points. If the Islanders lose on Thursday and the Canadiens earn a point against the New York Rangers the same night, the Islanders will be eliminated from the playoff race.
Toronto, meanwhile, would be eliminated if its loses in regulation on Thursday and Montreal earns a point against the Rangers.
The Maple Leafs kept their hopes alive with a 3-2 overtime win over the league-worst Flyers on Tuesday night. Toronto finishes the regular season at home against Montreal on Saturday.
"We know we're going to have to play better against the Islanders and Montreal to get a playoff spot," Leafs captain Mats Sundin said.
Bryan McCabe scored in overtime for Toronto, which allowed the Flyers to tie the game with less than five minutes left in regulation.
"Our season was on the line," Sundin said. "We obviously didn't have our best game. Sometimes there's nerves and guys are putting a little too much pressure on themselves. It's always tough - a lot of pressure for our team, none on their team. They come in with a lot of young guys eager to play.
"But, even though we didn't play a great hockey game, we showed a lot of character and we got the two points. It would have been easy for us to panic but we stuck to our guns and battled it out."
The Islanders helped themselves and the Maple Leafs with a 3-2 shootout win over the Rangers on Tuesday night, preventing New York's other team from clinching a playoff spot.
Still, because they have fewer victories than the other contenders, the Islanders likely need to win out to reach the postseason because total victories is the first tiebreaker in the NHL.
"Our backs are up against the wall, and will be the next three games," Islanders forward Ryan Smyth said. "We put ourselves in this situation, and tonight, we got ourselves out of it.
"We left it all on the ice tonight, and Dubie (Islanders goalie Wade Dubielewicz) won us the game. He always gives you that extra added confidence, and we have confidence in him. We've just got to protect the house to give him a chance. We battled hard for him, and he battled hard for us tonight."
The Islanders had lost four straight and eight of their previous 10 games before Tuesday's victory.
New York has won the last two meetings with Toronto in shootouts after the Maple Leafs won the season's first matchup.