Thomas Vanek and Jason Pominville also scored for Buffalo, in position to end the series Friday night in Buffalo.
Jason Blake and Mike Sillinger scored for the Islanders, and Rick DiPietro stopped 27 shots in his third start since returning from a concussion.
The Islanders thought they had tied it with 1:42 left after Miller was pushed across the goal line in a big scramble in front. Referee Mike Leggo, positioned behind the goal, immediately waved off the goal and his decision was upheld by replay.
Pominville then beat DiPieto with 1:12 left to seal the victory.
Drury, who also scored twice in Buffalo's Game 1 victory, gave the Sabres a 3-2 lead with a power-play goal 39 seconds into the second period. He scored from the slot off his own rebound after DiPietro and defenceman Tom Poti failed to control the puck.