Hibs started the match well and Chris Hogg had an excellent opportunity to give the Easter Road outfit an early advantage but he headed wide from David Murphy's fine cross.
Dunfermline then went even closer to breaking the deadlock on the ten-minute mark when they were denied by a combination of the woodwork and Hibs keeper Andy McNeil.
Jamie McCunnie let fly with a rasping effort that came back off the right-hand post, but McNeil did well to save the follow-up as James O'Brien fired in the rebound.
McNeil then pulled off another spectacular save to deny the Pars.
Former Aberdeen defender Phil McGuire almost netted against Hibs for the second week in succession as he fired in a dipping volley, but McNeil produced an acrobatic save to tip the ball over the crossbar.
Hibs dominated possession after the break and within minutes of the restart, Ivan Sproule fired over the bar from the edge of the area.
The Pars were content to hit on the break and this tactic almost paid dividends as Gary Mason was put though on goal by a neat flick from Adam Hammill, but Mason failed to take advantage by firing high and wide of the target.
Hibs almost snatched victory in the closing minutes of the match but they were denied by a goalline clearance from Souleymane Bamba.
Abdessalam Benjelloun fired in an effort on goal after Pars goalkeeper Dorus de Vries failed to claim the ball but Bamba did well to clear the ball to safety.