Their midweek loss to Aberdeen had brought the Glasgow giants' unbeaten start to the season to an end but they showed an emphatic return to form against the highlanders.
Griffiths grabbed his first ever goal at Celtic Park in the 11th minute with a close range effort before setting up Charlie Mulgrew to make it 2-0 in the 22nd minute.
The former Wolves striker sent a sizzling strike past Dean Brill in the 57th minute before the Inverness 'keeper somehow let a long-range effort from substitute Kris Commons squirm into the net 12 minutes from time.
Griffiths rounded off the scoring in the 85th minute when he calmly converted a bouncing pass from Commons to seal his hat-trick.
Celtic manager Neil Lennon said he got the reaction he was looking for from his players.
"I thought that was a fantastic performance from start to finish and with better finishing it might have been a bit more," Lennon said.
"I am delighted for Leigh Griffiths and he could have had a lot more."
His Inverness counterpart John Hughes said there was lots to learn from the defeat.
"One thing I will say is that we came here and had a go. We are having quite a good season and playing with confidence," Hughes said.
"There were some good passages of play for us but with our defensive record I am disappointed we have lost five goals. Even in defeat we have to learn and bounce back."
Inverness arrived at Celtic Park having not conceded in seven of their last eight away trips but their defence didn't hold out long as Griffiths converted an Emilio Izaguirre cross from three yards out to fire the hosts ahead.
Celtic didn't have long to wait for a second though with Griffiths this time turning provider in the 22nd minute. He sent in an awkward corner to the front post where Mulgrew managed to nick in and neatly back-flick the ball past Brill.
A good passing move from Inverness saw Billy McKay release Graeme Shinnie down the left wing but his ball into the box was scooped over by Ritchie Foran.
Inverness had Brill to thank for stopping Celtic extending their advantage when the keeper stuck out a foot to stop Anthony Stokes' shot after Mulgrew picked him out with a cutback from the by-line.
Griffiths should have increased Celtic's advantage three minutes after the break when Nir Biton played a perfectly weighted pass through the middle for the striker but, with only the keeper to beat, he sent his effort wide.
However, he made up for that miss in the 57th minute when he slammed home his second of the game. Griffiths nicked in between David Raven and James Vincent to steal the ball and burst into the box before smashing a superb left-foot shot that went in off the post.
The keeper was at fault when Celtic made it 4-0 in the 78th minute. Commons twisted and turned to lose two defenders before firing in a shot that Brill should have saved.
Griffiths sealed his hat-trick in the 85th minute when he took a touch to control a bouncing pass from Commons before sending a composed angled finish beyond Brill.