"Probably our best game all year when it comes to playing a full 60 minutes and everyone contributing," said Hagelin, who has scored in three of the last four games. "We definitely needed one of these just to feel good about ourselves."
The Rangers haven't posted consecutive wins since Nov. 21-23, and they were 2-8-2 in their previous 12 on home ice.
"We owed the fans this one. They've been supporting us quite a bit lately, and we haven't really produced for them," said Talbot, who improved to 7-2-0 and lowered his goals-against average to 1.67. "There is not a whole lot of time to think about it. Just go out there and try to carry this game into tomorrow."
While coach Alain Vigneault said he decided on Monday's starter, he kept his lips sealed. No. 1 goalie Henrik Lundqvist had started the previous seven games while compiling a 3.79 GAA.
"He's (Talbot) a young kid that's learning the NHL game," Vigneault said of the 26-year-old rookie. "He came in here and did what we expect of our goalies and gave us a chance to win."
New York -- which hasn't won consecutive home games since Nov. 6-10 -- now goes for a fifth win in meetings with Toronto (18-16-4), which is 2-5-1 in its last eight games. The Leafs have had an especially rough time on the road, getting outscored 35-19 during a 1-6-3 stretch since the start of November.
Toronto hits the road after suffering a 5-4 shootout loss to Detroit on Saturday. The Leafs, who were outshot 38-23, erased an early 3-1 deficit before coming up short.
"We'll take the point," said captain and defenseman Dion Phaneuf, who snapped a 25-game goalless drought. "Coming back, I feel that was a big step for our team to come back against a team that doesn't really give up a whole lot. We did a lot of really good things."
James Reimer was pulled after allowing three goals on 12 shots in the first period. Jonathan Bernier went on to stop 25 of 26 shots, but he surrendered two shootout goals in as many chances.
"It takes a toll on you trying to dig out of a two-goal hole like that," Joffrey Lupul, who had a goal and an assist, told the NHL's official website. "If we take one thing from the game, it's probably get off to a little better start."
Reimer, 1-1-1 with a 2.95 GAA against the Rangers, has gone 2-3-1 with a 3.79 GAA during an eight-game stretch overall. Bernier is 1-4-1 in his last six and 1-6-2 in his last nine on the road.
Lundqvist is 8-3-2 with a 2.20 GAA and two shutouts against Toronto since 2009-10.
The Rangers will need to be wary of Phil Kessel, who has four goals and five assists in his last seven games in the series. Kessel leads the Leafs with 33 points, 16 of which have come in 17 road contests.