Griffiths struck in each half as he lined up alongside Moussa Dembele, who was playing his first pre-season match following his move from Fulham.
Both strikers came close early on before Griffiths fired inside the near post from the edge of the penalty box in the 27th minute, after collecting an inside pass from Saidy Janko.
Celtic remained on top with Kieran Tierney and Liam Henderson – back from a loan spell at Hibs – linking well down the left and causing problems.
Dembele turned inside and forced a good stop from the goalkeeper seconds after the restart and the hosts missed a good chance before Griffiths was allowed room to fire into the corner of the net from 25 yards out in the 56th minute.
Miha Zajc finished brilliantly into the top corner from 16 yards two minutes later but Celtic had several chances to regain their two-goal lead, the best seeing Nadir Ciftci set up fellow substitute Ryan Christie to hit the bar from six yards.
Brendan Rodgers had started with both Stefan Johansen and Nir Bitton in midfield amid interest in their services from Galatasaray and Espanyol respectively.