Ennis skated into a rebound off the pad of Flyers backup goalie Michael Leighton and smashed the winner into the open net to give the Sabres a 3-2 lead in their best-of-seven series, with game six scheduled for Sunday in Buffalo.
"I saw it pop out," Ennis told reporters. "I tried to get to the net. I knew (Mike Weber) was shooting it -- just hoping he (Leighton) would kick it to me."
Ennis scored the Sabres first of three first-period goals, Buffalo racing to a 3-0 lead and chasing Philadelphia starter Brian Boucher from the net.
The goaltending change sparked Philadelphia, who roared back to tie the score early in the third period on goals by James van Riemsdyk and Andrei Meszaros in the second before Daniel Briere's equalizer.
"We were hard-charging, trying to fight back. We felt like if we could win that period, we could win the game. The guys did a really good job at unloading the tanks and getting back in."
Tomas Vanek and Marc-Andre Gragnani also scored for Buffalo.
In Anaheim, the Predators rallied from behind twice in the third period before Jerred Smithson secured the win with his goal 1:57 into overtime.
The Ducks looked poised to win the game on Jason Blake's second goal of the game with 5:46 remaining in the third but Shea Weber tied it up with just 36 seconds left with a rocket from the blueline.
(Reporting by Mike Mouat in Windsor, Ontario. Editing by Alastair Himmer)