Ennis, the 26th pick in the 2008 draft, earned a spot in the Buffalo lineup in place of injured right winger Drew Stafford.
"You dream of playing in the NHL, and that first goal was just indescribable," Ennis said. "It was really just extreme excitement hopping on the ice for the first time, a pretty awesome feeling."
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.
"I thought he [Ennis] played a great game," Sabres coach Lindy Ruff said. "He gave us some energy, he made a couple of great plays. He could have had a couple of goals in the game ... and he even took a run at [Chris] Pronger."
Pronger and Jeff Carter netted 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.
"They've been playing smart," Miller said of the defense. "Our defensemen don't allow the other team to get the puck where they want it. That sets everything up and makes it a little easier for all the other guys."
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.
"We made it harder by playing catch-up hockey with penalties in the first period," Flyers coach John Stevens said. "We got frustrated a little bit and allowed them to get a little momentum."
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.
Briere said that the Sabres were still thinking about the Flyers' 5-2 win in Buffalo on Nov. 6.
"I think their coaching staff used that game as motivation," said Briere, a former Sabres player.