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.
After Blake opened the scoring for the Islanders at 6:24 of the first, Vanek and Drury scored in a 1:48 span to give Buffalo a 2-1 lead. Vanek tied it with 8:43 left, beating DiPietro from the high slot off a rebound. Drury then slipped the puck past DiPietro from the edge of the crease off a feed from Dainius Zubrus.
Sillinger tied it at two on a power play with 16 seconds left in the period, beating Miller from the slot off Viktor Kozlov's pass from behind the goal.
Blake scored a second after a New York power play expired. After Miller stopped Blake twice and turned aside Miroslav Satan's close-range attempt, Blake took a cross-ice feed from Poti and beat Miller with a quick shot from the right slot.
Blake missed most of the second period after crashing headfirst into the boards late in the first. Buffalo's Teppo Numminen was penalized for boarding on the play, leading to Sillinger's power-play goal.
Notes: Vanek also scored Monday night at Nassau Coliseum in Buffalo's 3-2 victory in Game 3. ... The Islanders haven't advanced past the first round since reaching the conference finals in 1993. In their previous two playoff appearances, first-round matchups with Ottawa in 2003 and Tampa Bay in 2004, the Islanders split on the road only to drop the next two at home en route to five-game eliminations. ... The Sabres also won three of the four regular-season meetings against New York. ... Game 6, if necessary, will be Sunday night at the Coliseum.