The home side were dominant in the first half hour and made enough chances to win a handful of games.
But their finishing let the Pars off the hook and they only had a spectacular Derek Riordan goal to show for their pressure.
Garry O'Connor left Greg Shields trailing but couldn't find the target and then Stephen Glass was denied by a great save from Allan McGregor.
When Scott Brown failed to hit the target after a fine mazy run you wondered whether Hibs would ever score.
However, Riordan had Easter Road buzzing with a great strike on 17 minutes. O'Connor laid the ball into his path and without looking up he bent the ball into the top corner from the edge of the box.
But totally against the run of play Dunfermline levelled after 35 minutes from substitute Simon Donnelly's first touch of the ball.
Bartosz Tarachulski flicked the ball on and Donnelly ran beyond a square defence to slam home a low finish.
Hibs continued to be dominant after the break but McGregor made a great save from Kevin Thomson's volley.
However, the Pars keeper was helpless when Riordan produced another great shot the ease Hibs in front. Brown was fouled 20 yards from goal and Riordan struck a wonderful free-kick.
That seemed to settle Hibs and young substitute Steven Fletcher rounded things off with a thundering 20 yarder two minutes from time that hit the back of the net before the keeper moved.