After giving up three third-period goals, Miller stopped the final nine shots he faced in Buffalo's 4-3, series-ending victory Friday night.
Maxim Afinogenov scored the decisive goal as the Sabres hung on to win their third straight and eliminate the Islanders in five games.
It wasn't easy in a game that seemed to be over after the Sabres opened a 3-0 lead midway through the second period, and led 4-1 with 13:22 left.
New York scored two goals in three minutes, capped when Chris Campoli converted a rebound with 6:53 remaining. But then Miller shut the door.
Miller stopped 30 shots overall, his best coming on Miroslav Satan with 12 seconds left.
Satan cut across the crease and had Miller beat before the goalie spun around and stuck out his glove hand, getting enough of Satan's shot to turn it aside. Miller then scrambled to the side of the net to prevent Alexei Yashin from wrapping in the rebound.
The Sabres advanced to the second round for the second straight year and will face either the New York Rangers or Tampa Bay, should the Lightning get past New Jersey. The Rangers have already advanced after sweeping Atlanta.
Derek Roy, Drew Stafford and Jason Pominville also scored for Buffalo, which lacked consistency and at times looked little like the top-seeded team that led the NHL with 53 wins and 308 goals.
Satan and Campoli each had a goal and assist and Trent Hunter also scored for the Islanders.
It didn't help that hours prior to the game, New York learned it would be without Sean Hill. The veteran defenseman was hit with a 20-game suspension by the NHL earlier in the day for violating the league's drug policy.
Not much has gone New York's way since the Islanders won their final four games to sneak into the playoffs on the last day of the regular season.
The Isles were already upset after disputed goals went against them in each of their past two games - including a potential tying goal disallowed in a 4-2 loss in Game 4 on Wednesday night.
There was no disputing Afinogenov's deciding goal, which came on the transition and after Miller kicked out a shot. Thomas Vanek set it up, streaking up the left wing and burst past two defenders. Vanek then dropped a pass to Afinogenov, who slapped it in from the left circle. The Sabres appeared to take control when Pominville scored 39 seconds into the second period to make it 2-0, and Roy scored 11 minutes later. New York lost its fifth consecutive first-round playoff series, and hasn't advanced since reaching the conference finals in 1993.