Hibs paid the price for a slow start as they found champions Celtic just too good, Brendan Rodgers side two goals ahead in just 19 minutes before going on to seal victory.
The Capital side fought all the way despite those early strikes from Tom Rogic and Olivier Ntcham, a superb strike from Flo Kamberi 18 minutes into the second half giving them hope only for Odsonne Edouard to restore Celtic's two goal cushion.
Martin Boyle again cut the leeway to just one goal but Edouard claimed his second of the match with three minutes remaining to seal the points for Celtic, the French midfielder denied a hat-trick as an even later strike came back off the post - the fifth time Brendan Rodgers' players had struck the woodwork.
Hibs had a glorious opportunity to open the scoring after only two minutes when Celtic skipper Scott Brown brought down Emerson Hyndman a yard outside his penalty area, bringing not only a free-kick but a yellow card. However, Stevie Mallan, normally so dangerous from such an area pulled his shot wide.
Celtic, incredibly, hit the woodwork twice within the space of a minute, Edouard finding the outside of goalkeeper Adam Bogdan's left hand post after Callum McGregor's cross had eluded everyone before the Hoops midfielder sent in a free-kick after Darren McGregor, back for his first game since the beginning of August, was booked for a foul on James Forrest, the ball clipping the top of the cross bar.
But the home side took the lead in the eighth minute, Rogic playing a one-two with Forrest before curling the ball beyond Bogdan. Celtic really had the bit between their teeth, Ntcham drilling a shot just wide before stinging the palms of the Hibs goalkeeper with a vicious effort.
It was case of third time lucky for the Frehch player in the 19th minute when Rogic played an inviting pass into his path leaving him with the simple task of sliding the ball beyond Bogdan.
Celtic should have extended what was already a comfortable lead on the half-hour mark, Edouard forcing a good save from Bogdan only for the ball to fall for Scott Siinclair, who had replaced the injured Brown. But with an empty goal gaping he fired his shot against the post before Forrest drove the rebound wide.
Hibs boss Neil Lennon, who had started with a back three of Efe Ambrose, McGregor and Lewis Stevenson, was forced into adding to that back-line, Mark Milligan dropping in to play alongside McGregor in central defence with a midfield diamond.
Three minutes before half-time Celtic goalkeeper Craig Gordon was called into action for the first time, beating away a rising shot from Mallan as Hibs looked for a way back into the match. If that was easy enough for Gordon, he had to be at his best a minute later, going to his left to claw away a net bound Martin Boyle header from an Ambrose cross.
Bogdan went down bravely at the feet of Sinclair three minutes after the restart after Rogic and Forrest had carved out the opening for the Celtic substitute but Hibs were looking more comfortable in their new formation without really causing the champions too many problems.
And they almost got that touch of luck they needed when Vykintas Slivka's low shot took a deflection which left Gordon wrong-footed, the Celtic goalkeeper breathing a sigh of relief as the ball crept past his post.
Kamberi needed no such luck, though, as he pulled Hibs back into the match. Taking a pass from Daryl Horgan, the Swiss striker made himself a half-yard of space before lashing a superb left foot shot which flew past Gordon and into the top corner of the net.
Astonishingly, Celtic hit the woodwork for a fourth time, Edouard just too quick for Ambrose as he bore down on Bogdan, his low shot beating the goalkeeper but crashing back of the far post.
Edouard wasn't so unlucky two minutes later when Keiran Tierney's cut back left him with the easy task of knocking the ball home to restore Celtic's two goal cushion.
But Hibs weren't going to go down without a fight, Boyle again reducing the leeway as he sprinted clear to dink the ball over the advancing Gordon only for Edouard to end it once and for all as he claimed his second, and Celtic's fourth, of the game three minutes from time before hitting the woodwork once more as he was denied a hat-trick.
Celtic: Gordon, Lustig, Benkovic, Boyata, Tierney, Brown (Sinclair 21), Ntcham, Forrest (Chrisite 82), Rogic (Kouassi 72), McGregor, Edouard.
Substitutes: Bain, Simunovic, Gamboa, Morgan.
Hibs: Bogdan, Slivka, McGregor, Ambrose, Stevenson, Milligan (Whittaker 72), Boyle, Mallan, Hyndman Maclarern 87), Horgan, Kamberi.
Substitutes: Marciano, Bartley, Nelom, Shaw, Porteous.
Referee: Don Robertson