A third straight win keeps them in championship contention but Dunfermline's aim is simply to survive following their seventh defeat in eight games.
Despite firing only in spurts, Hibs had a sharper cutting edge than their hosts and in the 17th minute a dazzling run from Ivan Sproule ended with Allan McGregor pushing a curling Derek Riordan effort around the post.
Garry O'Connor was next to test the Dunfermline goalkeeper, but although the home side were lacking inspiration, an angled header from Andy Tod and a firmly struck free-kick by Lee Makel kept things interesting.
Hibs finished the first half strongly with Riordan narrowly missing the target with a dipping half volley.
Moments later Gary Caldwell and Sproule combined to set up Hibs' top scorer but his left-foot finish was blocked.
A similar move early in the second period gave Hibs the lead as Riordan and Sproule provided a simple tap in for O'Connor.
Substitute Simon Donnelly and midfielder Darren Young both wasted decent opportunities to equalise but the dismissal of former Hibs defender Yanic Zambemardi for two heavy challenges within a minute on Sproule saw the visitors dominate the final quarter of the game.
O'Connor exploited slack goalkeeping to beat McGregor at his near post and Hibs were glad of his second goal when Gary Mason pulled one back with a late header.