TORONTO (Reuters) - The Toronto Maple Leafs bagged two quick goals in the third period and held on for a crucial 4-3 comeback win over the Buffalo Sabres on Saturday to improve their chances at making the playoffs.

Trailing 3-2 after two periods, Toronto's Mikhail Grabovski and Phil Kessel scored during a 2:33 span early in the third for a Maple Leafs team desperately trying to clinch a playoff spot for the first time since 2004.

"The urgency showed up in the third period," Leafs coach Ron Wilson told reporters. "I'm very proud of the team not to cave in.

Rookie goalie James Rimer made 39 saves for Toronto, who moved to within four points of the last two playoff spots in the Eastern Conference, currently held by Buffalo and the New York Rangers.

His biggest save came with the game on the line in the third.

Buffalo's Thomas Vanek charged down the wing, but Rimer robbed him with his right pad, then stopped the Sabres' Brad Boyes on the rebound.

"You try to dig in a little more and be ready for anything," Rimer said. "It's hard to explain, you're just desperate to stop the puck."

The Leafs also seemed to have solved the puzzle that is Ryan Miller, recording a second win in a row over the Buffalo goalie, who still owns an impressive 24-10 record all-time against the Leafs.

"Get traffic in front of him, keep him deep, (and) make him work," said Wilson after Kessel's game-winner deflected off a Sabres defender.

Clarke MacArthur and Tyler Bozak delighted a sold-out Air Canada Center crowd by staking the Maple Leafs to a 2-1 lead midway through the second period.

Buffalo, which opened the scoring on Mike Weber's tally less than three minutes into the game, charged back on goals by Jochen Hecht and Jordan Leopold to regain the lead entering the third period.

But the Maple Leafs did not allow another goal.

"It was an important game for us, eight points back or four," Bozak said.

"We didn't want it to go to overtime. We knew we had to win this one to keep our chances alive. We had a good talk between the second and third and came out really hard."

(Reporting by Gene Cherry in Salvo, North Carolina; Editing by John O'Brien)