NEW YORK -- Justin Bailey scored his first NHL goal, and Anders Nilsson made 24 saves to help the Buffalo Sabres to a 4-1 win against the New York Rangers at Madison Square Garden on Tuesday.
Zemgus Girgensons, Evander Kane and Jack Eichel also scored, and Sam Reinhart had two assists for Buffalo (14-15-8), which had one win in its previous seven games.
"It's a good team win," Sabres coach Dan Bylsma said. "I think there was a lot of areas where we did well in the game tonight. In terms of how we want to play, I thought our defense did a simple but good job with their execution with the puck and moving the puck north and getting the puck up to our forwards. I thought it was probably our best game in the third period with a lead, playing the way we need to play."
WATCH: All Sabres vs. Rangers highlights
Nick Holden scored for the Rangers (26-13-1), who had won three straight. Henrik Lundqvist allowed four goals on 19 shots.
"I don't want to take anything away from the opposition, but there's no doubt that we didn't do a good enough job preparing our team for tonight's game," Rangers coach Alain Vigneault said. "I've mentioned many times that are no easy games in this League, and we weren't ready when the game started. Our execution was non-existent. We didn't have a [defenseman] that could make a pass, and our compete level was not good enough.
"I haven't said this very often with this group since I've been here, but this was a very bad game where we got outworked badly and we're going to need to respond here."
Video: BUF@NYR: Girgensons beats Lundqvist to open scoring
Girgensons gave the Sabres a 1-0 lead at 12:17 of the first period. William Carrier redirected Brian Gionta's shot from a sharp angle into the slot, where Girgensons collected the puck and put a backhand shot past Lundqvist.
Kane scored with 38.1 seconds remaining in the first, finishing a 2-on-1 with Reinhart by putting the latter's rebound past Lundqvist to make it 2-0. It was Kane's ninth of the season.
Bailey made it 3-0 early in the second, but Holden responded for New York with 4:05 left in the period when he one-timed J.T. Miller's feed for his eighth goal, fourth in as many games.
The Rangers outshot the Sabres 15-4 in the second period, but Buffalo entered the third unfazed and took a 4-1 lead on Eichel's power-play goal at 1:10.
New York was held without a shot on goal in the third until Oscar Lindberg was denied by Nilsson with 5:28 remaining.
Video: BUF@NYR: Kane crashes net, slips home rebound
Goal of the game
Bailey, a second-round pick (No. 52) by the Sabres in the 2013 NHL Draft, scored his first in the NHL 1:03 into the second period when he intercepted Kevin Klein's pass in the slot, then deked around Klein before putting a wrist shot past Lundqvist to give Buffalo a 3-0 lead.
"It was a huge relief," Bailey said. "I've had chances in the past, and I can't say it hasn't been on my mind all last summer and this year too. I'm just happy it finally came and I can start to get back to playing the way I play."
Video: BUF@NYR: Bailey beats Lundqvist for first NHL goal
Save of the game
With four minutes remaining in the first period, Nilsson positioned himself perfectly to stop Chris Kreider's redirection right in front after pass from Mats Zuccarello.
Video: BUF@NYR: Nilsson stones Kreider on the doorstep
Unsung performance of the game
Defenseman Zach Bogosian played the second-most minutes for the Sabres (22:08) and blocked four shots.
Highlight of the game
Eichel finished a tic-tac-toe passing play with Matt Moulson and Reinhart to help put the game out of reach. He redirected Reinhart's feed from the left circle past Lundqvist for his eighth goal.
Video: BUF@NYR: Eichel taps a power-play goal past Lundqvist
They said it
"It was fun to stand back in the third and see the way we play, the way we shut the door and shut them down. It was easy to be a goaltender in the third period for us." -- Sabres goalie Anders Nilsson
Video: BUF@NYR: Nilsson robs Stepan with big glove stop
"My big thing is, and what I think is such an important thing for our group, is when we aren't executing passes and executing our 1-on-1 battles and winning those, we put ourselves in a really tough spot. Everyone on the ice has to raise their level." -- Rangers center Derek Stepan
Need to know
Eichel extended his point streak to four games (three goals, two assists). … Sabres defenseman Josh Gorges did not play because of a hip injury. He was replaced by Taylor Fedun, who was recalled from Rochester of the American Hockey League before the game. … Rangers forward Matt Puempel missed the game because of concussion-like symptoms and is out indefinitely. Puempel was hit during New York's 6-2 win at the Colorado Avalanche on Saturday and experienced symptoms near the end of practice Monday. He was replaced by Nicklas Jensen.
Sabres: At the Chicago Blackhawks on Thursday (8:30 p.m. ET; NBCSN, CSN-CH, NHL.TV)
Rangers: At the Philadelphia Flyers on Wednesday (8 p.m. ET; NBCSN, TVA Sports, NHL.TV)
Video: Sabres cruise to 4-1 victory against the Rangers