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.
The visitors, playing in all black, looked ropey in the early stages, even before Hibs took the lead. Griffiths raced on to Paul Hanlon's long ball 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 Eoin 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.
Hibs 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.
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.
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.
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.
There was time for Williams to make another save, this time from Kayal, but the final whistle sounded with Hibs having held out for three points.