Hibs began on fire, Celtic goalkeeper Scott Bain taking a Daryl Horgan shot at the second attempt before the Irishman fizzed a ball across the face of goal and only inches out of reach of Stephane Omeonga, the Belgian Under-21 midfielder then forcing Bain to turn his effort round the post.
All that came in the opening six minutes followed by Paul Hanlon blazing a shot over after Darren McGregor had nodded a Stevie Mallan cross down to his feet.
Celtic, of course, aren't on the cusp of a an eighth successive Premiership title by allowing other teams to boss them around and Ofir Marciano had to rise to tip over a net-bound curling shot from Olivier Ntcham before the Hibs goalkeeper comfortably gathered Mikael Lustig's header.
Jozo Simunovic came to Celtic's rescue, sliding in to intercept Omeonga's pass as it threatened to find Marc McNulty in space before Marciano again got up well, finger-tipping Odsonne Edouard's netbound free-kick over the bar.
Edouard did put the ball into the net 13 minutes from time but was clearly offside as he latched onto Forrest's through ball.
Hibs were enfoced to endure a nervy five minutes of added on time, Tom Rogic firing a free-kick into the defensive wall from 20 yards out before Hanlon threw himself in front of Edouard's shot, conceding a corner from which Marciano pulled off the save of the game, once more throwing himself high to touch away Simunovic's header.
Hibs: Marciano, Gray, D McGregor, Hanlon, Stevenson, Milligan (Slivka 70), Horgan (Agyepong 83), Mallan, Omeonga, Kamberi (Shaw 70), McNulty. Substitutes not used: Bogdan, Bartley, Gauld, Spector.
Celtic: Bain, Lustig, Simunovic, Ajer, Izaguirre, Brown, Ntcham (Rogic 62), Forrest (Weah 85), C McGregor, Hayes (Sinclair 71); Edouard. Substitutes not used: De Vries, Toljan, Burke, Benkovic.
Referee: Nick Walsh