Ehrhoff's tally 43.4 seconds left in the third period was his second of the game for the Sabres, who broke a four-game losing streak.
Tyler Ennis also scored for Buffalo.
Ryan Miller earned the win with 36 saves in a game originally set for Jan. 7 but postponed by a storm.
Cam Ward yielded three goals on 18 shots.
Notable deaths of 2014 [PHOTOS]
Julius Randle breaks leg during NBA debut