Mika Zibanejad scored his third goal in three games and Igor Shesterkin made 34 saves for the Rangers (15-4-1). New York had a five-game home winning streak end and had gone 13-1-1 in its past 15 games.
"We didn't play the way that we wanted to play in order to be successful," Rangers coach Peter Laviolette said. "That's why we sit here where we sit right now. So, we need to reset and we need to be ready to play."
Peterka gave Buffalo a 1-0 lead at 11:41, whipping a high shot from inside the right face-off circle past Shesterkin's glove.
Tuch made it 2-0 at 19:33 of the second period, scoring from the slot off a rebound of Mittelstadt's shot from the right circle.
"We wanted to bring way more intensity and play at a level that we can play," Peterka said. "The other night wasn't our game. We knew that. We looked at the video and today we wanted to come out hot."
Luukkonen made 23 saves in the first two periods. But his best came at 3:35 of the third period, when he reached back with his stick and stopped Jimmy Vesey's shot from the left circle with the paddle.
"Sometimes, you get lucky and sometimes, you don't," Luukkonen said. "You try to follow the play as long as you can and this time, he hit the stick. Happy about that, but I will not be trying those in the near future."
Tuch said, "Huge save. Save of the year. I don't know what you want to call it, but I was on the bench and my jaw was on the floor until I got back on the ice."