After Rangers dropped two points against Hearts at home on Saturday, Neil Lennon's side capitalised by taking maximum points in Leith in their opening game.
Anthony Stokes opened the scoring with a close-range strike in the 14th minute following a mistake from Hibernian goalkeeper Graham Stack and Ki Sung-yueng doubled the visitors' lead with a drive just after the hour mark.
Stack made some amends when he saved Gary Hooper's penalty in the 68th minute but the visitors ran out easy winners.
Celtic have four friendly matches before their next SPL game but they look to be up and running.
However, on the evidence of their opening game, it promises to be a long, hard season for Hibernian who barely tested Hoops goalkeeper Lukasz Zaluska.
Celtic, captained for the day by Mark Wilson in the absence of suspended Scott Brown, went into the game as firm favourites.
Manager Lennon fielded a strong side with a midfield of Kris Commons, Ki, Beram Kayal and Joe Ledley, and Gary Hooper and Stokes in attack.
Defender Kelvin Wilson made his SPL debut, while Lennon's other new signings, Victor Wanyama and Adam Matthews, started on the bench.
Sean O'Hanlon made his SPL debut for the home side who made little impact in a rather uneventful first half.
The Parkhead side looked comfortable in the opening stages but it was Hibs midfielder David Wotherspoon who had the first effort on goal after eight minutes, albeit with an inswinging cross from the left that sped past Zaluska's left-hand post.
As the home side warmed to the task, the Hoops goalkeeper was called into action moments later when he had to cut out a dangerous cross from left-back Callum Booth, just before Kelvin Wilson did well to clear from inside his six-yard box and thwart lurking Hibs striker Garry O'Connor.
However, it was Stack who gifted Celtic the lead.
The home number one fumbled a looping free-kick from wide on the right by Commons, which allowed Stokes to gather at the back post and the Irishman quickly dispatched the ball into the roof of the net.
As Hibs tried to muscle their way back into the game, another cross by Wotherspoon had the Hoops defence momentarily undecided and glad to see the ball skip past the far post for a goal kick.
On the half-hour mark O'Connor used his bulk to retain possession under pressure from defender Glenn Loovens before sending Ivan Sproule racing down the right, but his cross evaded Wotherspoon who had failed to catch up.
Celtic started the second half strongly and in the 48th minute, after the Hibs defence had failed to properly clear a Mark Wilson cross, Commons tried a lob from the edge of the box which just missed the target.
Three minutes later and Hibs had their best chance of the game when Sproule latched onto Booth's through-ball which split open the Celtic defence.
A timely tackle by the recovering Kelvin Wilson on the Irishman as he raced into the box, chased also by Celtic left-back Emilio Izaguirre, brought hopeful shouts for a penalty from the home fans which referee Iain Brines ignored.
On the hour mark James Forrest came on for Commons, moments before O'Hanlon limped off to be replaced by David Stephens.
But in the 62nd minute the three points were secured when Ki drilled a shot low past Stack from the edge of the box.
Moments later, as the visiting fans continued their celebrations, O'Connor, albeit under some pressure from Loovens, missed Sproule's cross from the right eight yards from goal.
Celtic had the chance to increase their lead further when Sproule tripped Izaguirre in the Hibs box to concede a penalty.
However, Stack dived to his right to push Hooper's spot-kick against the post before helping to clear the rebound.
But that boost failed to inspire Hibs and they seemed to lack the belief that they could get back into the game.
Georgios Samaras replaced Stokes in the 78th minute to pose different problems for the Hibernian defence.
However, the game petered out - aside from another long-range effort from Ki which cleared the bar - leaving Lennon content with Celtic's almost perfect start to their title quest.