NEW YORK -- Jack Eichel was so upset after the Buffalo Sabres' loss to the Boston Bruins on Saturday that he stormed out of the locker room without addressing the media. The next day, he insisted the Sabres' season wasn't over and that they could still play better.

On Tuesday night, Eichel and Buffalo backed up those words.

Eichel was one of four goal-scorers and Anders Nilsson stopped 24 shots as the Sabres defeated the New York Rangers 4-1 at Madison Square Garden.

Buffalo had lost six of seven coming into the game while New York was riding a three-game winning streak. But it was the Sabres who started strong by limiting the Rangers to two harmless shots over the first 16 minutes and held the Rangers to zero shots over the first 15 minutes of the third period.

"This was kind of a rebound game for us," Buffalo coach Dan Bylsma said. "We were going on the road and playing a good team on the road and we've had some different injuries and different guys leaving the lineup for different reasons. I thought this was a good answer from our team and a good answer for a lot of different guys."

The Sabres (14-15-8) still sit at the bottom of the Eastern Conference but maybe this game could be a springboard to a postseason push.

Evander Kane and Zemgus Girgensons scored their ninth and fourth goals of the season, respectively, to put the Sabres ahead 2-0 at the first intermission. Rookie Justin Bailey scored his first NHL goal early in the second period to push the lead to 3-0, as he intercepted a poor pass from defenseman Kevin Klein and made a nifty move before beating Henrik Lundqvist, who stopped just 15 of 19 shots.

"You could tell the first 10 minutes of the game they were hungry," Lundqvist said. "They came with a lot of speed and desperation in their game. A lot of times, that's what's going to win you hockey games. They kind of set the tone in the first 10 minutes and they got some timely goals. (We) made some mistakes and it's my job to be there to clean it up, but was just not able to do that."

Rangers defenseman Nick Holden scored his eighth goal in the second period to trim the deficit to 3-1, but Eichel buried a power-play goal early in the third to sap any life the Rangers may have had.

"For the most part, we played a pretty simple game for 60 minutes and had success," Eichel said. "At times this season, we've gotten away from our game. You can see in the third period, we didn't really give them much at all. A lot of pucks were north and in their zone and it seemed like we played with it in their zone. We did a good job cycling, defense did a good job getting the puck north, our goalie made some huge saves and we got a win."

The Rangers were hampered by a poor start but also by a back end that committed too many turnovers and couldn't move the puck.

"We didn't have a D that could make a pass," Rangers coach Alain Vigneault said. Captain Ryan McDonagh was more troubled by the Rangers' recent inconsistencies, as they have followed two recent three-game winning streaks with sub-par showings resulting in losses.

"We owe it to ourselves as players, to our lines and pairs to prepare ourselves for every game, to execute, to give ourselves a chance," McDonagh said. "For whatever reason, we didn't do that tonight. It happened here too many times in this stretch and you know we're just about at the halfway point of the season, so if we don't find a way to bring that intensity and execution night in and night out, we're going to see ourselves fall off.

"Hopefully this is a lesson learned and a hard turning point for us."

NOTES: Sabres C Johan Larsson is out indefinitely after having surgery on his wrist and elbow. Larsson told a Swedish newspaper he will miss the remainder of the season. He has six goals and 11 points in 36 games. ... Sabres D Josh Gorges (hip) was unable to play despite being a game-time decision. ... Rangers LW Rick Nash (groin) missed his sixth straight game, although he practiced Monday. ... Rangers LW Matt Puempel (concussion) did not play. ... Rangers D Adam Clendening was a healthy scratch.