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The game went ahead in windy conditions despite concerns about Storm Boelo.
Marink Reedijk made two changes from the side that started last week against Falkirk, Jamie McGrath and Joe Newell replaced Azeem Abdulai and Martin Boyle.
Boyle had been listed in the starting XI but had to withdraw at the last minute due to illness. Youngster Zach Bruce was called into the squad and started on the bench.
Martin O’Neill also made one change with record signing Kasper Hogh replacing Haissem Hassan who dropped to the bench.
Sam Johnstone retained his place in goal while defenders Alistair Johnston and Cameron Carter-Vickers were listed as substitutes.
Felix Passlack led the team out despite club captain Newell starting.
The players from both sides showed their support for Show Racism the Red Card ahead of kick off.
Much of the South Stand lay empty as Celtic were provided a limited number of tickets and both the Pat Stanton and Famous Five Stands were sparsely populated due to a combination of the Block Seven ban and the weather.
Hibs started on the front foot and won a corner within 20-seconds when Liam Scales headed over a Passlack cross.
Then two minutes later they took the lead when Newell’s quickly taken free-kick caught out the Celtic defence and Owen Elding smashed a tremendous finish into the far corner.
The lead only lasted two minutes and Celtic equalised. Callum McGregor’s long-range effort was well saved by Raphael Sallinger and from the resultant corner Jason Kerr headed the ball into his own net.
Moments later Celtic almost took the lead when Hogh was inches away from connecting to Callum Osmand’s clever cross.
Osmand then set up Hogh again, but Sallinger did well to block his shot from close range.
At the other end Miquel Chaiwa tried a long-range effort that flew wide.
Passlack did well to intercept a Scales pass and his cross found Elding but the youngster’s shot was blocked.
Elding set up Josh Mulligan but Colby Donovan slid in to clear the danger.
A mistake by Donovan allowed Thibault Klidje a chance but his lob was too high.
Then just before the break Celtic took the lead when a tackle by Marko Ivezic on Osmand on the edge of the area was picked up by Camilo Duran, who cut inside onto his left foot and fired a devastating finish past Sallinger into the far corner of the net.
Hogh was booked for dissent after complaining when referee Ryan Lee blew for a free-kick on Duran instead of playing advantage.
McGrath limped off at half time but was still there when the teams came back out.
After the restart Klidje was booked for a foul on Donovan when Sallinger produced a great save to deny Mika Baur.
In the 51st minute the injured Donovan was replaced by Alistair Johnston.
Newell tried his luck after the ball fell to him on the edge of the area but his effort was blocked. The ball fell to Chaiwa but his long-range strike flew well wide.
Hibs enjoyed a spell of pressure without testing the Celtic goal and in the 62nd minute O’Neill decided to make a couple of changes with Hassan and Jota replacing Osmand and Hogh.
Hassan was quickly in action and a 20-yard strike went narrowly wide.
In the 66th minute Rabbi Matondo and Ante Suto replaced McGrath and Klidje.
Duran went close with a header from a Jota cross.
In the 71st minute Duran and Johnston were replaced by Cameron Carter-Vickers and Shim Mheuka.
Reedijk respoded by replacing Newell with Abdulai.
Kieran Tierney was shown a yellow card for a foul on Chaiwa who was quickly replaced by Grant Hanley who surprisingly went upfront.
Matondo had an effort which was blocked and eventually ended in the arms of the Celtic keeper.
Ivezic was booked for cynically stopping a counter attack.
Carter-Vickers did well to stop a goal-bound Mulligan effort as Hibs piled on the pressure looking for an equaliser.
But it was not to be and the visitors held on the secure the three points leaving Hibs at the foot of the table.
Hibs: Sallinger, Passlack, Ivezic, Kerr, Mayor, McGrath, Chaiwa, Mulligan, Newell, Elding, Klidje.
Substitutes: Smith, Hanley, Williams, Iredale, Cadden, Suto, Matondo, Abdulai, Bruce
Celtic: Johnstone, Donovan, Murray, Scales, Tierney, McGregor, Baur, Nygren, Duran, Hogh, Osmand.
Substitutes: Sinisalo, Johnston, Jota, Sorensen, Carter-Vickers, Oxlade-Chamberlain, Hassan, Mheuka, Forrest.