Home manager Brendan Rodgers had changed to three at the back to allow Leigh Griffiths to play alongside Moussa Dembele up front.
But Inverness kept them at bay until Scott Sinclair pounced to fire home after the break.
Griffiths tapped in before Caley Thistle's Greg Tansey was sent off and Tom Rogic blasted home the third.
That second yellow card, which came moments after the second goal, well and truly ended Caley Thistle's hopes of frustrating Celtic for a second time this season.
And Celtic, whose only dropped points this season came at Caledonian Stadium, cruised to a sixth straight domestic clean sheet to stretch their lead over Aberdeen, who have also played one game more than the reigning champions.
Celtic manager Brendan Rodgers decided to change his much-recognised shape following the midweek Champions League draw in Germany.
He opted for a back three and a front two of Dembele and Griffiths, but it was an experiment that only lasted for 13 minutes due to injury.
Mikael Lustig hobbled off with a nasty looking ankle knock after a tussle with Josh Meekings.
Dembele and Griffiths continued to link up, but Stuart Armstrong was ordered to fill in at right back.
The tinkering looked to upset the Celtic rhythm and, at times in the first half, they looked to be operating within themselves.
Caley Thistle manager Richie Foran said before the game that his side would press and frustrate the reigning champions and, for long spells of the first period, they did just that.
They closed Celtic down well and prevented them from finding the gear that would ultimately give them the lead.
But even the most pessimistic of the home supporters knew it was only a matter of time.
The chances were being created and the Inverness door was creaking.
The defences were breached early in the second half and the opening goal came courtesy of a now familiar and formidable name.
Sinclair latched on to a defence-splitting pass from Callum McGregor and blasted low past goalkeeper Owen fon Wiliams for his 10th goal of the season.
Griffiths was keen to impress in a rare start and he found the net after Dembele's effort was parried by Fon Williams.
Greg Tansey was given a second yellow card for a foul on McGregor in the build up and that killed off any slim hopes of a Caley Thistle come back.
Rogic came off the bench to add a third, but with Lustig and captain Scott Brown hobbling off, the win may well have come at a price.
Match ends, Celtic 3, Inverness CT 0.
Second Half ends, Celtic 3, Inverness CT 0.
Attempt saved. Iain Vigurs (Inverness CT) left footed shot from outside the box is saved in the centre of the goal.
Foul by Jozo Simunovic (Celtic).
Jake Mulraney (Inverness CT) wins a free kick in the defensive half.
Corner,  Celtic. Conceded by Brad McKay.
Attempt saved. Patrick Roberts (Celtic) left footed shot from the right side of the box is saved in the bottom right corner.
Attempt missed. Tomas Rogic (Celtic) left footed shot from the centre of the box is close, but misses to the left.
Attempt missed. Stuart Armstrong (Celtic) right footed shot from the right side of the box is close, but misses to the right.
Goal!  Celtic 3, Inverness CT 0. Tomas Rogic (Celtic) left footed shot from the centre of the box to the centre of the goal. Assisted by Stuart Armstrong.
Attempt blocked. Patrick Roberts (Celtic) left footed shot from outside the box is blocked.
Substitution, Inverness CT. Larnell Cole replaces Liam Polworth because of an injury.
Delay in match Liam Polworth (Inverness CT) because of an injury.
Foul by Leigh Griffiths (Celtic).
Liam Polworth (Inverness CT) wins a free kick in the defensive half.
Attempt blocked. Scott Sinclair (Celtic) right footed shot from outside the box is blocked.
Foul by Tomas Rogic (Celtic).
Iain Vigurs (Inverness CT) wins a free kick in the defensive half.
Corner,  Celtic. Conceded by Gary Warren.
Foul by Leigh Griffiths (Celtic).
Iain Vigurs (Inverness CT) wins a free kick in the defensive half.
Attempt blocked. Tomas Rogic (Celtic) right footed shot from the centre of the box is blocked.
Stuart Armstrong (Celtic) wins a free kick on the left wing.
Foul by Jake Mulraney (Inverness CT).
Attempt missed. Stuart Armstrong (Celtic) right footed shot from the right side of the box is close, but misses to the right.
Callum McGregor (Celtic) wins a free kick in the defensive half.
Foul by Iain Vigurs (Inverness CT).
Substitution, Celtic. Tomas Rogic replaces Moussa Dembele.
Hand ball by Stuart Armstrong (Celtic).
Corner,  Celtic. Conceded by Josh Meekings.
Second yellow card to Greg Tansey (Inverness CT) for a bad foul.
Callum McGregor (Celtic) wins a free kick in the defensive half.
Foul by Greg Tansey (Inverness CT).
Goal!  Celtic 2, Inverness CT 0. Leigh Griffiths (Celtic) left footed shot from the right side of the six yard box to the bottom right corner.
Attempt saved. Moussa Dembele (Celtic) right footed shot from the centre of the box is saved in the centre of the goal.
Foul by Nir Bitton (Celtic).
Iain Vigurs (Inverness CT) wins a free kick in the attacking half.
Substitution, Inverness CT. Jake Mulraney replaces Billy King.
Substitution, Inverness CT. Alex Fisher replaces Lonsana Doumbouya.
Substitution, Celtic. Nir Bitton replaces Scott Brown because of an injury.
Celtic restored their 10-point lead at the top of the table after overcoming Inverness Caledonian Thistle.