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.
Celebrity Families of 2014 [PHOTOS]