The visitors did create some chances, most notably in the first half, but once Celtic went ahead just before the interval the result was never in doubt.
The home side's first goal was a tragedy for Darren Dods as he turned the ball into his own net under pressure from Jan Vennegoor of Hesselink.
If there was doubt over who got the final touch for the first goal, there was none about Celtic's second as the Dutchman clinically swept home with 20 minutes remaining.
Celtic was unable to relax and substitute Jiri Jarosik finished the scoring with a looping header five minutes from the end.
Michael Fraser made two good early saves from Maciej Zurawski and Vennegoor of Hesselink which settled his nerves in only his second start for Inverness.
The visitors were dangerous on the break and Artur Boruc did well to block a Grant Munro shot from a corner.
Inverness were lucky to survive an incredible scramble on their goal-line after Vennegoor of Hesselink's header, though Graham Bayne should then have done better than glance his header wide at the other end from six yards.
After Dods' own goal, the writing was on the wall for Caley Thistle.
Celtic pushed the visitors further and further back in the second half and Vennegoor of Hesselink crisply slid home Paul Telfer's excellent cross to double the lead.
There was still time for Jarosik to head home Shaun Maloney's driven corner, but by that time Celtic were already looking ahead to their mouth-watering Champions League clash with Manchester United on Tuesday.