The on-loan Wolves striker struck in the eighth minute when he rounded Hoops keeper Fraser Forster and squeezed the ball in from an acute angle.
The visitors dominated almost totally thereafter but huffed and puffed when not being denied by Hibees keeper Ben Williams, who had a fine afternoon.
Although Eoin Doyle had two good chances before the break to double the home side's lead with Gary Deegan missing another in the second-half, these three points belonged to the Leith side's resolute rearguard who could have seldom withstood such a battering.
Celtic travelled to Edinburgh having built up a head of steam with six successive wins but manager Neil Lennon made three changes to his starting XI with defenders Thomas Rogne and Mikael Lustig and striker Lassad Nouioui in for Charlie Mulgrew, Beram Kayal and Tony Watt with the latter two dropping to the bench.
Hibs showed two changes to the side which began the 1-0 home defeat to Ross County on Boxing Day.
Pat Fenlon drafted in defender Lewis Stevenson and midfielder Jorge Claros for David Wotherspoon and Ryan McGivern, the former starting as substitute.
The visitors, playing in all black, had Efe Ambrose, Rogne and Kelvin Wilson as their back three in a 3-5-2 formation which looked ropey in the early stages, even before Hibs took the lead.
Two minutes after Lustig's free-kick from 25 yards was comfortably saved by Williams, the home side were ahead as the Celtic defence again hesitated.
Griffiths raced on to Paul Hanlon's long ball chased by Rogne and when Forster raced out to meet him, the Hibs striker took the ball wide of the keeper before sliding it with great composure into the net from almost on the bye-line.
That goal was not in the Celtic script but in the 12th minute Hibs should have been two ahead when Doyle met a long Griffiths free-kick with his head six yards out his limp effort went straight to Forster.
The champions fought back and Gary Hooper hit the post from a Georgios Samaras pass but the flag was up for offside and as the game swung from end to end, Griffiths was also flagged as Doyle's cross-cum-shot evaded him at the back post.
In the 24th minute, with the Parkhead side beginning to turn the screw, Rogne headed a Lustig corner over the bar.
Celtic had changed to 4-4-2 with Ambrose moving into midfield and it was his mazy run towards the Hibs box where he was fouled by Gary Deegan, which earned the Leith midfielder a booking and brought the next chance for the visitors.
However, Lassad's curling free-kick from 25 yards went high over the bar.
Hibs, increasingly ragged and occasionally desperate, could hardly get out of their own half as Celtic pressed hard for the leveller.
However, four minutes from the interval Doyle missed another great chance he blazed over the bar from 12 yards with only Forster to beat, after getting the break of the ball.
There was no let up from the Parkhead men when the second half started and in the opening minutes the ball flew in and around the Hibs box, without finding any takers.
The home side could find no respite yet in the 55th they had another good chance when Griffiths took a Doyle pass and laid it off to Deegan but he seemed to stub his toe in his attempted shot from 10 yards and the ball trundled through to Forster.
Moments later, there was an appeal for a penalty when Doyle was challenged by Emilio Izaguirre in the Celtic box but referee Craig Thomson pointed for a goal kick.
It seemed a matter of time before the champions and SPL leaders would draw level.
In the 77th minute midfielder Victor Wanyama's 30-yard drive screamed just over the bar, before Williams made a decent save from Paddy McCourt, who had replaced Lassad, with skipper Scott Brown knocking the rebound over.
Moments later, after Ambrose had scooped the ball over from close range, Williams made a great save from Hooper, clawing his shot away from 14 yards for a corner which the Hibs' rearguard again defended.
There was time for Williams to make another save, this time from Kayal, who had earlier come on for Rogne, and somehow the final whistle sounded with Hibs having held out for three points.