The Hoops suffered their first league defeat in 31 matches at Aberdeen in midweek but they never looked like slipping up in a match in which Charlie Mulgrew and Kris Commons were also on target.
Griffiths opened the scoring after 12 minutes when he nipped in at the front post to meet a super Emilio Izaguirre cross and volley into the roof of the net.
The striker turned provider on 22 minutes when his low corner caught three Inverness defenders flat-footed and Mulgrew flicked the ball into the net at the front post.
And Griffiths sealed the victory on 57 minutes when he pounced on the ball at the edge of the box and crashed a first-time drive in off the post.
Commons (78) came off the bench and quickly got his name on the scoresheet as he shuffled his feet to create enough space for a dipping drive from 25 yards which slithered under the keeper.
Griffiths completed his treble with four minutes remaining as he got in behind the defence to latch on to a Commons pass and shoot across Dean Brill.
Inverness almost pulled a goal back on 30 minutes when Graeme Shinnie exchanged passes with Billy McKay and delivered the ball into the box but Richie Foran was unable to take advantage on the stretch and scooped over the bar.
Brill then denied Tony Stokes with an outstretched foot to keep out a powerful drive from the Irish striker after Mulgrew strode forward and set up the opportunity.
Griffiths should have doubled his tally four minutes after the interval when he put the ball wide of the target with only Brill to beat after Nir Biton created the chance with a wonderful pass.