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The leaders started brightly and Griffiths fizzed a shot narrowly wide inside the first five minutes, before Adam Rooney saw a header saved at the other end.
The defender rose highest from a corner to power a header home and give Ronny Deila's men the advantage at the break.
Celtic were awarded a penalty after the hour when Stefan Johansen was brought down inside the area, and Griffiths made no mistake from 12 yards to double his side's lead.
Mackay-Steven wrapped up the points with just over 20 minutes remaining when he rattled in an effort off the post from the edge of the box.
Johansen then claimed the fourth 10 minutes from time when swept home Adam Matthews's cutback to put the gloss on an emphatic win.