Ivan Sproule gave the visitors an interval lead with a 37th-minute strike, and striker Garry O'Connor doubled the advantage six minutes after the break.
However, Dunfermline midfielder Ryan Thomson pulled a goal back a minute later, before defender Paul Hanlon appeared to deflect Jason Thomson's effort into his own net to hand the Fifers a point.
Lashing rain and live television coverage were likely factors in the crowd being a low 4,116 for a match which saw the visitors begin in positive style.
In the fourth minute, following a Martin Scott corner from the right, the ball fell to Sproule who cleared the bar by some distance with a snatched shot from eight yards.
The encounter quickly degenerated into little more than a frantic series of challenges and misplaced passes with neither side gaining control.
In the 16th minute Dunfermline defender Jason Thomson sent Andy Kirk into the box but the ball ran away from the striker near the byline and his attempted cut-back was easily mopped up by the Hibs defence.
Two minutes later the Leith men were cut open again when Pars midfielder David Graham sent Jason Thomson through but his unconvincing drive from 10 yards hit the sidenetting.
The home side had a clear chance in the 27th minute following a corner from the left by Joe Cardle.
Hibernian failed to clear their lines and the ball was helped on to Pars defender Alex Keddie by Ryan Thomson, but a half-hearted volley from 10 yards limped past Graham Stack's right-hand post.
Dunfermline by that point had the edge, but in the 34th minute Kirk had to stretch too far at the back post to get his head on a searching Cardle cross and the ball flew wide.
Three minutes later, though, and out of the blue Sproule struck for Hibernian.
With the Pars defence all over the place as Hibs came down the right, O'Connor fed the Northern Irishman and from 10 yards he slid a shot past Paul Gallacher and into the far corner of the net.
After a swift counter-attack seconds from half-time Sproule had another effort deflected wide for a corner but it came to nothing.
The second half did not take long to show an improvement.
Three minutes after the break Stack did well to stop Austin McCann's deflected cross creeping in at the top corner, and Keddie almost got on the end of Cardle's corner which flashed across the six-yard box.
Moments later O'Connor should have made it 2-0 when he was put clean through by Griffiths, however Gallacher got down to his left to push the sidefooted drive around the post for a corner.
Sproule flighted the ball in from the right and Sean O'Hanlon's header was goal-bound until McCann headed the ball off the bar.
But Hibernian had the bit in their teeth and in the 51st minute O'Connor slammed a shot from the edge of the box past the flailing Gallacher and was then booked for taking his shirt off in celebration.
A minute later Dunfermline were back in the game when Ryan Thomson ran along the edge of the Hibernian penalty area before leaving Stack was flat-footed with a low shot.
The home fans shouted for a foul when Cardle went to ground in a challenge with Richie Towell but referee Calum Murray was having none of it.
Andy Barrowman then replaced Kirk before heading a Graham cross over the bar from barely five yards out, then O'Connor and Griffiths were surprisingly replaced by Akpo Sodje and Junior Agogo respectively and the double substitution seemed to quickly backfire.
In the 63rd minute Dunfermline levelled when Stack parried a Cardle shot into the air for Jason Thomson to volley back across the goal, and the ball came off Hanlon and flashed into the net.
Both teams went looking for a winner which provided an enthralling finale.
In the 78th minute Barrowman again missed the target with a header, this time from a Jason Thomson cross, before Stack made another decent save down low from Cardle.
There was to be no more scoring but Dunfermline could claim plenty of pride as Colin Calderwood's struggle at Hibs continues.