Miller turned aside 10-of-11 shots in the final period, keeping the Sabres in it as they went on to win their second straight in a long shot bid for an Eastern Conference playoff berth.
Buffalo, with 59 points, remained seven points out of the eighth and final spot in the East.
The Islanders had to play without starting goalie Evgeni Nabokov, who like Coach Jack Capuano, missed the game with the flu.
Replacement netminder Kevin Poulin turned aside 35 shots and Frans Nielsen tallied for the Isles.
Notable deaths of 2014 [PHOTOS]