"We're alive," Maurice said of the Leafs, who trail the Flyers by seven points for the final playoff spot in the Eastern Conference. The teams meet again Wednesday night in Philadelphia.
Daniel Briere scored 1:12 into the third period to give Philadelphia a 3-0 lead but Mats Sundin, Kubina and Jeremy Williams scored to tie it.
"I liked the courage we showed and the character in coming back like that," said Sundin.
Scottie Upshall and Braydon Coburn scored for Philadelphia.
Kubina threw the puck out from behind the goal and had it go in off a Flyers defenseman for the game-winner.
Toronto really wanted to win in regulation.
Maurice pulled goalie Vesa Toskala with more than a minute left to play and the Leafs on a power play. Philadelphia didn't come close to scoring on the empty goal at the other end.
"He was coming out regardless," Maurice said of Toskala. "(There are) two factors, one you are aware of the potential (to score), so you ask the people around you. They are 50-50 on that.
"The down side is the puck is in your net, you lose the game and I'm standing up here not feeling so fresh."
Flyers goalie Martin Biron made 51 saves.
The Flyers are being chased by five teams - they lead Buffalo by four points - and could ill-afford the third-period collapse against Toronto.
"We just played with way too much panic in our game," Philadelphia coach John Stevens said. "You have to have the courage to play. You have to have the courage to take people on 1-on-1. You have to have the courage to play a hockey game. To go out there and play panicky like we did tonight, throwing the puck away and not moving our feet, it was ridiculous."
The Maple Leafs outshot the Flyers 13-4 in the first period but were down 1-0. Upshall opened the scoring at 13:26 after getting behind Leafs defenseman Anton Stralman and taking a nice cross-ice pass from Vaclav Prospal. It was the seventh straight game the Maple Leafs allowed the first goal.
Coburn floated a point shot over a screened Toskala with 54.8 seconds to play in the second period while on a power play to give the Flyers a 2-0 lead. Toskala finished with 22 saves.
Briere made it 3-0 just 1:12 into the final period.
That gave Philadelphia a 2-0 lead at the second intermission and signaled bad things for the home team - the Flyers entered the game with a record of 25-1-1 when leading after 40 minutes.
Despite that, they couldn't keep Toronto from rallying.
"They kept putting pressure on us, kept taking chances, and it paid off for them at a key time in the game," Biron said. "That pressure made it hard for us to do a lot of the little things."
Notes:
Sundin has 16 points in his past nine games ... Antero
Niittymaki made 54 saves in goal for the Flyers during a win in
Toronto on Jan. 5.
