Reo Hatate’s penalty late in first half saw Celtic ahead at the break before the floodgates opened in the second half.
A stunning Elie Youan volley levelled the game only for Hyeongyu Oh to put the visitors ahead once more just moments later.
Daizen Maeda was then red carded for Celtic and seconds later so too was Jake Doyle-Hayes before a VAR intervention reduced his to yellow.
With the numerical advantage we laid siege on the Celtic goal and Kevin Nisbet celebrated his 100th Hibs appearance by netting the equaliser from the penalty spot with just 16 minutes left.
The boys never stopped and scored twice more before the end thanks to goals from Youan and Paul Hanlon to claim a famous win.
Lee Johnson made two changes to his starting XI from the weekend with Lewis Miller and Doyle-Hayes replacing Chris Cadden and Josh Campbell.
The match burst into life straight from kick-off with Youan going close twice in the opening 30 seconds as he was denied by Scott Bain at his near post before stabbing a second effort just wide.
Celtic would race up the park and almost score themselves as Alexandro Bernabi picked out Oh only for the Japanese to shoot over.
On seven minutes Liel Abada peeled off the right flank and his rising left shot from the edge of the box had to be tipped over the bar by David Marshall.
Both teams were committed to attack as play raged from end-to-end at breakneck speed.
On 11 minutes Doyle-Hayes robbed possession from Yuki Kobayashi on halfway before we worked the ball wide left to Lewis Stevenson and from his cross Nisbet was denied by a fine save from Bain.
The pace was relentless from both teams and from Bernabi’s cross Oh’s glancing header struck the crossbar.
The Celtic striker did well moments later to hold off CJ Egan-Riley before curling an effort towards the far post that was beaten away by Marshall at full-stretch. Abada was the quickest to react and should have scored from the rebound however, he dragged his shot across goal and wide of the far post.
Five minutes before the break Celtic were awarded a penalty kick when Stevenson tripped Callum McGregor as he tried to latch onto a Maeda cut back. Hatate calmly sent Marshall the wrong way to put his side ahead,
Campbell replaced Jeggo at the interval as we again started brightly with Bain called into action to deny Nisbet at his near post in the opening minutes.
On 52 minutes we deservedly levelled. Campbell’s cross was only partially cleared by Anthony Ralston to Youan who struck a sensational left foot volley past the helpless Bain.
Bain did well to gather a looping header from Campbell moments later before Celtic countered and Oh stabbed in from close range to restore his side’s lead.
Then on 66 minutes Celtic were reduced to 10 men after Maeda took out Will Fish to earn a second yellow card.
It appeared we were also going to play with ten men when Doyle-Hayes was shown a straight red card just seconds after the restart for a challenge on Oh however, a VAR review saw this reduced to yellow.
With 19 minutes remaining Stevenson’s ball down the wing saw Nisbet shrug off Carl Starfelt and put Youan into a great shooting position. The Frenchman opted to shoot early and his effort was beaten away by Bain.
Three minutes later we were awarded a penalty kick after Ralston hauled down Fish inside the six-yard box at a corner kick. Nisbet stepped forward to calmly send Bain the wrong way and claim a goal on his 100th appearance for the Club.
We were on top going into the closing stages and substitute Ewan Henderson was not far away from scoring against his former club with a curling effort that was just over the top.
Seconds later we were ahead for the first time this evening as Bain spilled a long-range squiggler from Youan.
Celtic were toiling to contain us as we poured forward at every opportunity and with four minutes remaining we scored our fourth of the evening as club captain Hanlon got in on the act by heading past Bain at his near post.
11 minutes of additional time came and went without Celtic having an effort on goal as we comfortably held on to claim a thoroughly deserved victory.
Three points this evening mean we go into the final game of the season just two points behind Saturday’s opponents Hearts with the chance of finishing fourth.
Hibernian: Marshall, Miller (Cadden 87’), Hanlon, Doyle-Hayes (Bushiri 87’), Newell (McKirdy 73’), Jeggo (Campbell 46’), Nisbet, Stevenson, Youan, Fish, Egan-Riley (Henderson 64’). Substitutes not used: Johnson, Cabraja, Hoppe, Devlin.
Celtic: Bain, Ralston, Starfelt, Kobayashi, Bernabei, Iwata (O’Riley 64’), McGregor, Hatate (Turnbull 64’), Abada (Forrest 64’), Haksabanovic (Maeda 22’), Oh (Kyogo 81’). Substitutes not used: Hart, Taylor, Jota, Welsh.
Referee: Kevin Clancy.
Attendance: 18,171.