The striker netted a sublime goal – his 14th of this campaign – early on in what proved to be a thoroughly compelling encounter and it ultimately proved enough to separate the two sides.
The agreement with Wolves to keep the prolific forward at Easter Road expires next month and, after another special moment from him secured an unexpected win, club officials will be doing their damndest to extend it.
"I will sit down with the chairman next week and discuss his situation," said manager Pat Fenlon. "Leigh has obviously scored a lot of goals and we are anxious to keep him. We are doing as much as we can."
Neil Lennon, the Celtic manager, could have done with one of his players producing a finish of a similar standard to the one Griffiths conjured up on what was a hugely frustrating afternoon for him. Lennon had made three changes to the side that had started in the 2-0 win over Dundee at Dens Park on Boxing Day; Beram Kayal, Charlie Mulgrew and Tony Watt dropped out and Mikael Lustig, Lassad Nouioui and Thomas Rogne all came in.
Rogne slotted into the middle of a three-man defence with Efe Ambrose operating to the right of him and Kelvin Wilson to his left. The opening goal suggested they were uncomfortable with having one less body in the back line.
Paul Hanlon played a speculative punt upfield in the ninth minute and Ambrose should really have cleared or controlled it. However, he failed to do either, Griffiths raced in and stole possession and then slotted his shot beyond Fraser Forster from an implausibly acute angle.
"It was a great finish," enthused Fenlon afterwards. "He still had a lot to do when he went around him. But he is capable of that. He is capable of finishing from all sorts of different angles."
The home team had the chance to build on their surprise early lead shortly afterwards when they won a free kick on the left flank. Paul Cairney floated a cross into the visitors' area and Eoin Doyle met it with a downward header. His effort lacked power and Forster saved easily. Celtic enjoyed the majority of possession and pressure thereafter in the first half. But, for all their endeavour, they were unable to create any decent chances for their strikers, Gary Hooper and Lassad Nouioui. Ben Williams in the Hibs goal remained untested.
The Scottish champions reverted to a back four at the start of the second half. Ambrose, who had been responsible for his team conceding the goal, was pushed forward into central midfield alongside Victor Wanyama and Scott Brown moved wide right. Switching to a 4-4-2 formation appeared more to their liking.
"I was disappointed with the way I set up the team early on," admitted Lennon. "I will take the blame. On another day we would have won comfortably. We just lacked an edge in front of goal"
Celtic looked to be highly fortunate when referee Craig Thomson waved away appeals for a penalty from Hibs players on the hour mark after Emillio Izaguirre appeared to bring down Doyle inside his own area. Lennon threw on Paddy McCourt for Lassad and Kayal for Rogne. McCourt definitely brought a spark to his team's play going forward. He was unfortunate not to net the equaliser in the 79th minute, his goal-bound shot blocked well by Williams.
The keeper came to his side's rescue again four minutes later after a neat interchange between Wanyama and Hooper sent the latter clean through. The Englishman's shot was brilliantly swiped clear by his compatriot for a corner.
A miserable day for Celtic was capped late on when Ambrose squandered the opportunity to net from a few yards out as an empty net beckoned invitingly. Having been on a wretched run and having lost 1-0 at home to top-flight newcomers Ross County on Boxing Day, few could have foreseen Hibs winning. It was hugely timely given that they do battle with city Hearts on Wednesday afternoon.
"The players will take huge confidence from this result," stated Fenlon. "Over the last three or four weeks people have started to doubt us. This has answered our critics a little bit."