It took Celtic only three minutes to get over any hangover from their midweek defeat at Ibrox as Chris Sutton, on his return from injury, netted from close range.
However, a surprise in the Celtic line-up was the return of Magnus Hedman in goal for David Marshall. The Swedish keeper had an excellent game capping his performance with a fine penalty save from Barry Wilson as Inverness threatened a fightback.
It was Hedman's first game since the Champions League match last December against Lyon and he must now have a chance of playing in the Old Firm game next Saturday.
Celtic went two up through John Hartson early in the second half and the Welsh striker added a third near the end to give Celtic a rather flattering final scoreline.
Undoubtedly sterner tests lie ahead against Rangers and Barcelona, and Celtic will have to improve on recent performances if they expect a positive return from those matches.
The home team opened the game brightly and it was no surprise when they took an early lead with a well-worked goal.
Hartson wandered across the 18-yard line before finding Aiden McGeady whose delicate chip was headed powerfully home by Sutton from six yards.
Thistle were finding it difficult to get out of their own half and Jackie McNamara and Sutton both shot over as Celtic closed in for the kill.
Indeed the home team should have been two up in the tenth minute. Hartson's header found McNamara whose return pass left the striker clear in front of goal but, from no more than eight yards, he blazed his shot over perhaps not realising how much time he had.
Russell Duncan made a good break for the visitors and from his cross Graham Bayne got between Bobo Balde and Hedman but was unable to take advantage.
Neil Lennon then made a timely interception to deny Barry Wilson.
The atmosphere was very subdued and McNamara was booked for a badly timed tackle on Juanjo.
Hartson was marginally offside from Alan Thompson's pass when Celtic looked certain to score.
In the best move of the first half, Lennon's superb pass released Thompson and his throughball inside Ross Tokely found Henri Camara but the striker's fierce shot was parried by Mark Brown and the keeper then did well to block McNamara's effort in the ensuing scramble.
Balde nearly allowed Bayne in with a short back-pass as nerves appeared to take hold of the Celtic rearguard. Juanjo shot wide with two half-hearted efforts before the visitors nearly equalised on the stroke of half-time.
Roy McBain's free-kick from wide on the right dipped and swerved before scraping past the far post as Hedman looked on helplessly.
The Inverness side continued to look for an equaliser at the start of the second half and an audacious 35-yard effort by Russell Duncan had Hedman back-tracking rapidly as he held his shot under the bar.
Just as Thistle began to believe they could salvage something from the game, Celtic went two ahead.
McNamara's cross from the right did not appear to carry any threat until Sutton flicked it on to Hartson who swept his shot home from six yards.
The points appeared safe for Celtic as they threatened to run riot. From Hartson's pass Thompson jinked his way into the box before Brown made a fine save from his effort and then did well to block a McGeady shot.
Grant Munro, who had a superb game for the visitors sweeping at the back, made an excellent tackle on Camara as the Celtic forward threatened to burst into the box.
Thistle then had their best spell of the match and threatened the Celtic goal on several occasions. McBain's pass to Wilson gave the winger room and time for his shot, but his effort swerved wide.
Wilson then neatly lobbed Lennon before hitting a 30-yard shot which Hedman at full stretch turned round his post.
Stuart Golabek followed this with an equally powerful shot which Hedman again saved before Thistle were awarded a penalty in the 75th minute.
Stan Varga impeded Richard Hart as he broke into the box and was booked for his tackle. Wilson, who had scored from his three previous spot-kicks, tried to wrongfoot the keeper but Hedman saved well diving to his right.
Three minutes later Celtic wrapped up the points. McGeady's pass found McNamara who skipped round Brown before crossing for Hartson to head home from almost on the line.
MAN OF THE MATCH: Neil Lennon (Celtic) - The midfielder broke up many attacks from the visitors and was always there to urge on his team-mates when the game fell flat.