Neil Lennon's side had lost their 26-match unbeaten league record at Aberdeen in midweek with a 2-1 defeat, but when the 23-year-old striker opened the scoring in the 11th minute with his first goal at Celtic Park since signing from Wolves in January, the threat of a repeat was removed.
The lively Griffiths then set up Charlie Mulgrew for his goal with a corner in the 22nd minute before thundering in a drive past Dean Brill in the 56th minute to end the game as a contest.
Kris Commons, on for Anthony Stokes, made it 4-0 in the 77th minute with a long-distance drive which squirmed through the fingers of Caley's over-worked goalkeeper, before Griffiths slipped in number five with five minutes remaining on a day when the margin of victory should have been much greater.
But it was a good day's work for the champions, who marked the 20th anniversary of Fergus McCann's takeover of the club, where the Canada-based businessman rescued Celtic from the brink of bankruptcy before restructuring the finances and redeveloping the stadium.
McCann's stewardship was based on prudence, a virtue not appreciated by many Hoops fans of that era who had to endure the dominance of rivals Rangers, although time had proved to be a great healer.
Former chairman Brian Quinn came on to the park to say a few words in tribute before the game, earning a laugh from the Hoops fans when he stopped to put on a 'bunnet' - the headwear so closely associated with McCann.
There was more for the Celtic supporters to be pleased about when Griffiths pounced five yards from goal to knock in a fine delivery from left-back Emilio Izaguirre despite the best efforts of Brill.
Inverness had only themselves to blame for Celtic's second. The Highlanders were caught sleeping when Griffiths swept in a rather ordinary looking corner to the front post from the right, allowing Mulgrew to flick the ball in from six yards.
In the 28th minute Caley skipper Richie Foran was presented with a good chance when left-back Graeme Shinnie put the ball on a plate for him 12 yards from goal, only for the Irishman to scoop his effort high over the bar.
The home side, though, remained dominant and had a couple more chances before the break to increase their lead.
In the 35th minute Mulgrew set up Stokes but his carefully-placed shot from 14 yards was blocked by Shinnie.
And moments later Mulgrew himself had a chance but failed to catch his drive well enough to cause Brill too much trouble.
Four minutes into the second half Griffiths was left with only Brill to beat from 12 yards after good work from midfielder Nir Biton, but the former Hibernian forward was far too casual with his finish and curled the ball past the far post.
However, he more than made up for that when he nipped in front of the hesitating Caley defenders David Raven and Gary Warren before arrowing a powerful shot high past Brill and in off the post.
In the 63rd minute, with most of the Inverness defence posted missing, Griffiths missed a great opportunity for his hat-trick after he ended a series of one-twos with Stokes by flashing his drive over the bar.
It had become a matter of how many Celtic would score.
James Forrest's cross from the right clipped the bar before Brill pushed his goal-bound shot past the post for a corner, with the spell of pressure ending when Griffiths fired wide from 16 yards.
Brill was at fault for Celtic's fourth when he allowed Commons' long-distance drive to slip through his fingers, before the Celtic midfielder played in Griffiths to slip the ball past the Caley keeper to claim the match ball.