The Sabres had plenty of energy in their third game in four nights, scoring the first goal and rallying from a 2-1 deficit in the third period. Tyler Ennis and Steve Ott scored, and Girgensons put Buffalo ahead with his goal early in the third.
Ryan Miller made some tough stops after giving up two quick goals in the second period, finishing with 38 saves in Buffalo's second win in 10 games.
Phoenix followed one of its best games of the season with a shaky performance.
David Moss scored his first goal in 17 games for the Coyotes.