Australia playmaker Tom Rogic came off the bench for the Hoops on 70 minutes but it was Griffiths making all the headlines for the league leaders.
Griffiths missed the target with a penalty in the 26th minute - his fourth failure from the spot this season - as a remarkable display by Well goalkeeper Connor Ripley kept the visitors at bay until the Parkhead striker eventually got the breakthrough just before the interval.
Ex-Celtic and Socceroos frontman McDonald levelled on the hour mark, but Ripley undid all his good earlier work when he allowed Griffiths's shot to slip through his legs for the striker's 37th goal of the season which took Ronny Deila's side eight points clear of Aberdeen going into the split.
Celtic can now prepare for the Scottish Cup semi-final against Rangers at Hampden Park secure in the knowledge that their fifth consecutive title win is all but sealed.
Other SPL results
Hamilton Academical 2 - 1 Dundee FC
Kilmarnock 3 - 0 St.Johnstone
Ross County 1 - 0 Partick Thistle
Dundee United 0 - 2 Inverness CT
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