Jason Pominville, Chris Drury and Thomas Vanek also scored for the Sabres. Buffalo swept the four-game season series against the Hurricanes, the team that beat the Sabres in the Eastern Conference final last season en route to the Stanley Cup.
Craig Adams spoiled Miller's shutout bid with a short-handed goal late in the third.
Carolina entered the game with a season-best, five-game win streak.
The Hurricanes' John Grahame finished with 22 saves in his second start in three games, and first against the Sabres this season. Cam Ward had started the three previous games against Buffalo, posting a 4.25 goals-against average in the three losses.