Celtic failed to build on their equaliser and found the home side resolute in defence to ensure the visitors dropped their first points of the season after six straight wins.
The performance and result will give Hibs some much-needed confidence before both sides meet in the Betfred Cup semi-final at Hampden Park in November.
After making eight changes for the 5-0 win over Championship side Partick Thistle in midweek, former Hibs manager Neil Lennon returned to the side which started against Kilmarnock last weekend with skipper Scott Brown and attackers Essonne Edouard and Christie among the big guns back in the side.
Former Hoops midfielder Allan took a fine reverse pass from Jackson to split the visitors' defence with a delivery down the right channel to Doidge and when he fired the ball across goal Ajer inadvertently diverted it past Parkhead keeper Fraser Forster at the near post.
The champions levelled after Kevin Clancy blew for a foul for a challenge on Forrest by Tom James about 60 yards from the Hibs goal.
With boos from home fans still ringing around the ground, and the Edinburgh side dropping their guard, Celtic right-back Moritz Bauer was sent down the right by midfielder Olivier Ntcham and when he floated a cross into the box Christie rose almost unchallenged to head high past Maxwell.
Heckingbottom was sent packing for his reaction and then Jackson went off with a head knock to be replaced by veteran defender Steven Whittaker.
Celtic midfielder Ntcham was perhaps fortunate to get only a yellow card for raising hands to Josh Vela after a tangle with both players booked.
Forster made saves from Stevie Mallan and Doidge – one either side of the break – as the match occasionally threatened to boil over.
In the 63rd minute Celtic unsuccessfully claimed for a foul when Christie was challenged by Hibs defender Lewis Stevenson inside the box, close to the byline and play raged on.
Edouard headed a cross from substitute Jonny Hayes, on for Ntcham, over the bar before he was replaced by Vakoun Issouf Bayo.
Celtic pressed hard for the winner in the closing stages and in the 84th minute Callum McGregor's shot from 12 yards was plucked out of the air by Maxwell before Hayes, Brown and Bayo all drove efforts over the bar.