Enroth sprang into action when Ryan Miller came down with a sinus infection and had to be held out. He responded with his first win since November 2011, turning aside 32-of-33 shots.
The Sabres also got a goal from Thomas Vanek while Andrej Sekera helped out with two assists.
Derek Stepan provided the only goal for New York -- a short-handed tally -- and Henrik Lundqvist made 19 stops.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys