Mike Webber fired a slapper that knocked off Michael Leighton's pad. Ennis swooped in from the right side and scored his second goal of the game.
Game 6 is Sunday in Buffalo.
The Sabres survived after blowing a 3-0 and chasing Flyers starting goalie Brian Boucher.
Thomas Vanek and Marc-Andre Gragnani also scored in the first period for the Sabres, and Ryan Miller made 36 saves. Danny Briere tied it for Philadelphia at 3:36 of the third period. James van Riemsdyk and Andrej Meszaros scored in the second.