Miller, who is in his ninth season with the Sabres, has had five shutouts in each of the last three seasons.
Thomas Vanek scored twice in Buffalo's third straight victory. The Sabres are off to a 5-1 start this season.
The game was scoreless until Vanek picked up his fifth goal of the season on a wrist shot 2:33 into the second period. Jason Pominville scored on a tip-in with 3:04 to go in the middle stanza and Vanek produced a power-play goal on a slap shot with 2:29 to go in the third.
Florida scored seven goals against Tampa Bay Monday, but has been shut out in its two games since then. Washington defeated the Panthers 3-0 Tuesday.
Jose Theodore gave up the three goals on 38 shots.