After Kris Commons cancelled out Darryl Westlake's opener at Celtic Park, substitute Griffiths took his league tally to nine for the season with a 20-minute treble.
Westlake looked to have put Kilmarnock on course to end a three-match losing run in the Premiership when his shot took a telling deflection and evaded Craig Gordon.
However, Commons got the champions back on track with a hooked finish shortly before the hour.
It was then the Griffiths show as he scored within five minutes of replacing James Forrest.
The former Wolves man added Celtic's second 10 minutes from time with a fierce drive that clipped the post before calmly picking his spot to round off the scoring with 85 minutes on the clock.
It leaves Kilmarnock ninth while Celtic take another step towards a fourth consecutive Scottish title.
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