Rangers boss Pedro Caixinha named a starting XI featuring seven players taking part in their first Glasgow derby and it was a chastening experience for most of them.
Celtic pinned their neighbours back for much of the opening exchanges and the only surprise when Australia international Rogic found the breakthrough was that it took 50 minutes to arrive.
Rangers could only partially clear a Griffiths corner from the left and Roberts scuffed a shot from the edge of the box. The ball evaded a cluster of blue shirts and Rogic pounced, pivoting to smash left footed into the roof of the net.
Griffiths' sixth goal of the season arrived a quarter of an hour later and Brendan Rodgers' champions are already eight points better off than their rivals after seven matches.