Dunfermline had taken the lead through a hugely controversial first half Kallum Higginbotham penalty but James Keatings pulled them level before Grant Holt secured the points from the spot after team-mate Andrew Shinnie had been bundled over by the Pars Lee Ashcroft.
And in added-on time substitute Brian Graham met Shinnie's cutback to slam home a third for the Hibees. But there was still enough time for Dunfermline substitute Michael Moffat to be sent of for aiming a kick at Shinnie.
Keatings went close to giving Hibs the lead with a superbly struck free-kick from 25 yards which clipped the top of Sean Murdoch's cross bar.
But the Pars stunned the Edinburgh club by going ahead in the 21st minute through a highly contentious penalty. Higginbotham's initial corner was cleared but the ball was relturned to the winger who sent in a hanging cross. Hibs goalkeeper Ofir Marciano flapped but Paul Hanlon got his head to the ball only for referee Alan Muir to point to the spot. He had seen a push which had sent Andy Geggan to the turf, the official immediately finding himself surrounded by an angry pack of Easter Road players.
Muir, though, was never going to change his mind and Higginbotham stepped up to send |Marciano the wrong way. Dunfermline could have doubled their lead two minutes later when Gavin Reilly's pass found Farid El Alagui all alone and onside but the former Hibs striker saw Marciano get down to save.
Hibs should have been level six minutes from the interval when Shinnie drove in a low ball from the right which Keatings missed at the front post and then Holt at the back stick before Fraser Fyvie had Murdoch at full stretch to turn over his free-kick.
The Capital club went even closer five minutes after the restart, Darren McGregor nodding Fyvie's free-kick back across goal for Hanlon at full stretch to get his head to the ball which came back off the base of Murdoch's right hand post before the goalkeeper clawed it to safety.
But they did get back on level terms, Higginbotham losing possession outside his own penalty area allowing Keatings to cut across the edge of the box before unleashing a rising shot which took a deflection off Nat Wedderburn before hitting the back of the net.
It was all Hibs and they went ahead in the 65th minute as Ashcroft clearly pushed Shinnie over in the box, leaving Holt to step up and slam the ball home from 12 yards.
Keatings lasted only a few more minutes, coming off second best as he attempted to block a Dunfermlline clearance, limping off to be replaced by Martin Boyle.
Dunfermline: Murdoch, Talbot, Martin, Ashcroft, Richards-Everton,Geggan, Wedderburn, El Alagui (Hopkirk 67), Reilly, Paton (McMullan 81), Higginbotham (Moffat 69).
Substitutes not used: Hutton, Williamson, McCabe, Fordyce.
Hibs: Marciano, McGregor, Hanlon, Fontaine; Gray, Shinnie, Fyvie, McGinn, Stevenson; Keatings (Boyle 547, Holt (Graham 88).
Substitutes not used: Laidlaw, Bartley, Forster, Graham, Harris, Cummings.
Referee: Alan Muir