The Sabres (11-25-9) also got goals from Kyle Okposo on the power play, and Justin Falk. Robin Lehner made 30 saves. Sam Reinhart and Jack Eichel each had two assists. Okposo also had an assist.
Buffalo has lost five of its past six games in regulation.
"It's really disappointing because once the guys got their feet under them in the first period they played a really good game," Sabres coach Phil Housley said. "On a couple of those goals, we are in our own zone and we are eager to do something big instead of taking care of our own end and staying behind the puck. If you take [the last] two goals away, our team played terrific."
Nash, who has 13 goals this season and 429 in his 1,035-game NHL career, has tried to tame his frustration over not scoring as much as he has in the past by focusing on being a reliable player in all three zones.
However, he has been around the net a lot and leads the Rangers with 145 shots on goal, 41 more than anyone else. That he's finally seeing some of them go in has created a necessary pressure release for him.
"You look on the chance sheet every night and you have three or four 'A' chances and the pucks just weren't going in," Nash said. "Then you get a game like [Thursday] where you get two good chances and they both go in. What I've been telling myself is, 'Stick with it, keep getting on the inside and keep helping the team, whether it's PK, defensive game, bringing the energy.' I know I'm supposed to score goals, but if you're not scoring you have to bring something to the table.
"At the end of the day I'm supposed to score goals, so it's nice to chip in that way."
Falk scored his first of the season at 17:10 of the second period to tie the game at 2-2. Miller scored his 10th goal, and second in as many games, at 8:26 of the second to give the Rangers a 2-1 lead.
Nash gave New York a 1-0 lead with a breakaway goal. Okposo tied it with a power-play goal at 18:41 of the first.
