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.
Two minutes after Mikael Lustig's free-kick was comfortably saved by Williams, the home side were ahead as the Celtic defence hesitated. 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 home.
Shortly afterwards Hibs should have been two ahead when Eoin Doyle met a long Griffiths free-kick with his head six yards out, but 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 Thomas Rogne headed a Lustig corner over the bar.
However, four minutes from the interval, Doyle missed another great chance as he blazed over the bar from 12 yards with only Forster to beat after getting the break of the ball.
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 Nouioui, with skipper Scott Brown knocking the rebound over.
Moments later, after Efe 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 still time for Williams to make another save, this time from Beram Kayal and somehow Hibs held out for three points.
Elsewhere, second-placed Inverness shared a goalless draw with St Johnstone at McDiarmid Park, while Motherwell were held by Kilmarnock at Fir Park.
Aberdeen beat Dundee 3-1 with a stunning hat-trick from Niall McGinn, with only substitute Mark Stewart able to score for the hosts.
- Sports & Recreation
- Fraser Forster
- Mikael Lustig