Thomas Vanek and Paul Gaustad also scored for the Sabres, who never trailed and won their third straight game.
Chris Pronger and Jeff Carter scored third-period goals for the Flyers.
Miller (12-2-1) was aided by a strong Buffalo defense that constantly thwarted the Flyers from in-close. He was at his best midway through the second period when he stopped Danny Briere and Scott Hartnell on the doorstep on successive flurries.
Vanek put the Sabres ahead during a power play at 3:11 of the first period with a one-timer from the slot.
Ennis made it 2-0 at 14:50 of the second, sending a wrist shot from just below the left circle that sailed under the armpit of Ray Emery, who made 22 saves.
Ennis, the 26th pick in the 2008 draft, was inserted into the lineup for right winger Drew Stafford. Stafford sustained a hip flexor injury Friday night against Calgary while playing in his 200th NHL game.
Ennis was recalled from Portland of the AHL and arrived in Philadelphia about 90 minutes before the game.
Pronger brought the Flyers to within 2-1 at 2:43 of the third when he snapped a shot through a screen, but Gaustad restored Buffalo's two-goal edge at 6:25 on a power play.
Carter scored a short-handed goal during a skirmish in front of the net at 10:21 to again bring the Flyers within one goal.
NOTES: Philadelphia LW James van Riemsdyk was scratched (flu). ... Flyers D Ryan Parent returned after missing four games (lower body). ... Sabres RW Jason Pominville hit the post during a power play late in the first period.