Miller stopped 29-of-31 shots, making several big saves down the stretch and ensuring a key victory for the Sabres as they attempt to gain an Eastern Conference playoff spot.
Hecht's goal 4:45 into the final period gave Buffalo a 3-1 lead and Brad Boyes, who was obtained from St. Louis this week in a trade-deadline deal, scored in his Sabres debut.
Tyler Myers scored and Andrej Sekera added a pair of assists for Buffalo.
Erik Christensen and Artem Anisimov scored and Henrik Lundqvist made 23 saves for the Rangers, who hold the seventh playoff spot in the East.
2014: The Year in Music [PHOTOS]