And both have key tests on Tuesday night. The Leafs, who are 11th in the Eastern Conference but only two points behind Carolina, the New York Islanders and Montreal, play host to the Hurricanes. The Canadiens are at home against the sixth-place New York Rangers.
The six clubs battling for sixth, seventh and eight place in the East - the Rangers, Tampa Bay, Carolina, the Islanders, Montreal and Toronto - are separated by only five points with two weeks left in the regular season.
The Leafs, Islanders and Hurricanes each have a game in hand over the Canadiens, Rangers and Hurricanes.
"You look at the schedule and you have a number in your head, but you figure you just win them all and that will make it easier," Leafs coach Paul Maurice said Monday in Toronto. "We just might have to.
"We have to win our head-to-heads, or get help. In terms of controlling your own (destiny), you just have to win those head-to-head ones that are so important."
That starts Tuesday night against the defending Stanley Cup champion Hurricanes, who are on a three-game winning run.
The Leafs are coming off a see-saw week in which they posted big wins over Ottawa and Buffalo between an ugly loss in Buffalo on Friday in which they blew a 4-1 third-period lead.
"In those last two games, we've come out strong and forced the issue," added Maurice. "(Tuesday) is going to be a little bit different because they're going to be a rested team.
"That's the game they play. It will be a bit of a battle of wills out of the gate."
The Leafs play four times this week, including games Thursday at Atlanta, Saturday at home against Pittsburgh and Sunday against the Rangers in New York.
The Montreal-New York matchup has two hot clubs on a collision course.
The Rangers have won five in a row, but Montreal has won four straight and has won its last six at home.
And while Rangers goalie Henrik Lundqvist was named first star of the week in the NHL on Monday, Canadiens rookie Jaroslav Halak got third star for his three wins in goal.
"Every game gets bigger and bigger and this one, against a team we're chasing for that final spot, is the same," said Montreal defenceman Sheldon Souray.
"It's important that we come out with the same effort we have in a while. We've just worked hard and kept it simple and it's worked. It's a tough game. Their goaltender is playing well and they're in the same boat as us."
The Canadiens are 0-2 against the Rangers this season, including a 4-0 loss in New York on Feb. 27. The two teams meet again April 5 in New York.
The Rangers play lowly Philadelphia between their meetings with Montreal and Toronto.
The Islanders play three of the conference's top clubs - New Jersey, Ottawa and Buffalo - this week, while Tampa Bay has a lighter week, at least on paper, with games against Florida, Carolina and Washington.
After Toronto, the Hurricanes play in Philadelphia and at home against Tampa Bay and Florida.
With so many teams involved, the race is still far too early to call, said Canadiens veteran Mike Johnson.
"I thought that with six games left, I'd be able to break it down and say who's going to finish where, but it's just too hard," said Johnson. "Too many teams are too close.
"And teams play each other, so there's three-point game implications. Maybe after this week we'll have a clearer picture, but it's so close, you can only worry about your own team now."
The Islanders got a huge point when they tied their game with the Rangers in the third period on Sunday, even though they eventually lost 2-1 in overtime.
In the West, the battle for the eighth and final playoff spot is a two-team affair, with the Calgary Flames holding a five-point lead over the ninth-place Colorado Avalanche.
The Flames are on a three-game winning run but have a tough week with games Tuesday and Thursday night in Minnesota, which is battling the Canucks for the Northwest Division lead, and a game Saturday in Vancouver.
The Avalanche play Tuesday night in Vancouver, then are in Phoenix on Thursday and at home Saturday against the Wild.