Buffalo tied the game late in the first on a power play goal from Kyle Okposo that was answered by J.T. Miller midway through the second period. The Sabres again tied it late in the middle frame on a goal by former Ranger Justin Falk.
Nash put the Rangers ahead for a third time before Rasmus Ristolainen evened things again with a power play goal with 5:01 left in regulation was followed by Buchnevich's 12th of the season.
Henrik Lundqvist finished the game with 34 saves, and saved his best for last with a critical save on Ristolainen in the dying seconds with the Rangers on the penalty kill.
The victory was a big one for the Rangers, who now embark on a week-long, four-game road trip through Colorado and California.
"We said we needed this one," Lundqvist said. "It's a game where I feel like if we play on top our game we're a good team. We're holding on to pucks tonight and our forecheck was better. Just like last game, start to recognize our group here.
"It's been a little up and down the past few weeks," he added, "but the last two have been good."
The 12-game goal drought for Nash seems like a distant memory following his back-to-back multi-goal performances this week.
"I hope they come in bunches," said Nash who now has 13 goals this season. "It's funny how the game works. Sometimes you get five or six opportunities a night and you don't score. Other times you get two chances and you put both in. It's a funny way, but you've got to stay level headed and you've got to stay with it."