By Alasdair LamontBBC Scotland at the Tulloch Caledonian Stadium
Celtic blew Inverness away with a great performance, before late slackness cost them a more comprehensive win.
They were quickly out of the blocks as Victor Wanyama headed in from Adam Matthews' corner.
Tony Watt curled in the second and battered in the fourth, with a well-worked move allowing Charlie Mulgrew to slot past Ryan Esson in between.
Ross Draper fired in two late goals to take the edge off Neil Lennon's joy and perhaps Terry Butcher's ire.
Lennon's side had struggled in the Highlands against Ross County last week, but there was never any threat of a repeat.
The visiting manager had expressed a desire pre-match for his side to start the game well, and he got his wish as Gary Hooper nutmegged Simon King before firing in a fierce shot, which Esson did well to push away.
It was from the resultant corner that Wanyama leapt to head emphatically past Esson, though the marking was suspect.
Celtic's lead was almost doubled on seven minutes after a hefty Draper challenge was penalised and Mulgrew crashed the free kick off the top of the crossbar from 25 yards.
The home side had spent virtually the entire first quarter of an hour on the backfoot, but Aaron Doran served notice of their ability on the offensive, bringing out a decent save from Fraser Forster with a long-range drive.
But as Caley Thistle pressed for an equaliser, Celtic picked them off on the counter-attack.
Mulgrew cleared from his own goal-line, it was helped on by Emilio Izaguirre and Wanyama to Filip Twardzik, who threaded the ball through to Watt. The striker drifted past King and curled the ball coolly beyond Esson.
Terry Butcher was infuriated by the ease with which Celtic were able to play through his side, but they almost got a goal straight back as Doran's cutback found Andrew Shinnie inside the six-yard box, but the striker poked the chance wide.
Watt might feel he should have had a second goal seven minutes before the break.
Hooper played a beautiful pass into the path of Twardzik down the left channel and when the young Czech rolled the ball across goal, Watt looked certain to score, but the angle beat him and he found only the side-netting.
Butcher no doubt had some harsh words to say to his players at the interval, but they were rendered meaningless after just three minutes of the second half.
A free kick earned by Hooper on the left side of the penalty area was rolled by Matthews into the path of Mulgrew, who side-footed into the bottom right-hand corner of Esson's net.
Watt again came within inches of a second goal after getting the better of Esson, but though he missed out on that occasion, he didn't have to wait too long to notch Celtic's fourth, rifling in from eight yards after good play down the left by Izaguirre.
Celtic took their foot off the gas, perhaps feeling they had earned the right to do so, but they were punished.
Draper burst into the box with nine minutes remaining to beat Forster at his near post and four minutes later he latched on to Conor Pepper's chipped pass to beat Forster at the second attempt.
That late slackness aside, there was plenty to please the Celtic manager, while his Caley Thistle counterpart will look to address some of his team's defensive frailties.
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