Richter kept the Rangers in the game, making 22 of his 36 saves in the second period. But he fell behind, 3-2, when Alexander Mogilny beat him with a one-timer 3:48 into the third.
"I think Richter played the kind of game we all know and have seen him play before," Rangers captain Mark Messier said. "When we need him the most, whenever this team had gone on a roll, he's been the guy who's done it. We expected the kind of game we got from him tonight."
"I've been feeling pretty good this year for most of the time," Richter said, "but it's a team game, and sometimes certain aspects of your game are going to have to pick up to help the team, and I didn't feel I was doing enough. Tonight I felt better. It felt good to help out the squad."
The Rangers capitalized on a turnover by the Maple Leafs to rally for their first win since October 15.
With the game tied, 3-3, rookie defenseman Carlo Colaiacovo attempted a pass to Travis Green on a late rush. But the puck was intercepted by New York defenseman Sylvain Lefebvre, starting the pivotal rush.
Lefebvre fed Rem Murray, who carried through the neutral zone and found Bure. The "Russian Rocket" beat Toronto goaltender Ed Belfour between the pads with a soft shot for his third goal in two games against the Leafs this season.
After Bure's goal, Richter faced one more test. Mats Sundin won a face-off from Eric Lindros and passed to defenseman Bryan McCabe, who was all alone in the low slot. But the blue-liner's slap shot was smothered by Richter.
"This was huge," Rangers right wing Mikael Samuelsson said. "It hasn't gone well for both teams. It was good we got one on the road. Richter played unbelievable tonight. He kept us in the game, and we kept digging and digging, and snuck one in late in the game and won."
In a game that featured all sorts of sloppiness and undisciplined play, the Leafs were slighty worse than the Rangers.
New York forged a 3-3 tie less than five minutes before Bure scored when Samuelsson put in his own rebound.
After firing a hard shot from inside the right faceoff circle, Maple Leafs defenseman Karel Pilar failed to pick up Samuelsson, who breezed through the slot and beat Belfour.
Prior to scoring the tying goal, the Rangers had taken three careless penalties, and with defenseman Dale Purinton off for hooking, the Leafs cashed in.
On the ensuing face-off, Petr Nedved was kicked out and replaced by Murray, who lost the draw to Sundin. Sundin fed Mogilny, who was alone in the slot and scored.
Nedved had tied it, 2-2, just after Shayne Corson was kicked out of a face-off with Lindros and penalized for cross-checking. Following a few cross-ice passes, Nedved found himself alone at the doorstep and beat Belfour.
The Leafs took a 1-0 lead with 3:07 remaining in the first when Mogilny centered a pass for Mikael Renberg, who put it home.
But it took just 1:50 into the second for Messier to tie the game after he intercepted Pilar's clearing pass.
Toronto, which has won just once since a season-opening win at Pittsburgh, fell to 0-3 on its season-high seven-game homestand.
"It was a heartbreaker to lose the game like that," Belfour said. "It was a slap in the face."
"He (Richter) made some great saves," Renberg said. "I think we could have had a bigger lead than one goal. He made some key saves. But still, we had the lead, and couldn't keep it."