The decisive moment arrived four minutes after the break when Anthony Stokes set up Guidetti who netted with a rising shot from inside the box.
It was the Swede’s ninth goal in seven games although the visitors were unhappy, claiming that Scott Brown had committed a foul in the build-up to the goal.
And the hosts were forced to hang on as Inverness created a number of decent chances in the closing few minutes.
As Caley chased an equaliser Danny Williams fired over from 15 yards, Graeme Shinnie shot wide and Greg Tansey blazed over, while Carl Tremarco missed with a header before home keeper Lukasz Zaluska smothered an effort by Billy McKay.
In a goalless first half, Zaluska was called into action inside 90 seconds, saving well from Graeme Shinnie whose 25-yard strike caused a few problems for the Celtic keeper.
At the other end, Guidetti fired narrowly over the bar, while Stokes missed a brace of half-chances.
And just before the break Shinnie fired over from 22 yards after good work from Danny Wiliams.
However, early in the second half, Celtic went ahead when Brown found Stokes whose pass was collected by Guidetti and the in-form striker lashed home, leaving Dean Brill with no chance.
Yet the visitors were furious with referee Craig Thomson who they believed missed a shirt pull by Brown on Williams.
Celtic’s win takes them into third spot in the table and above Caley on goal difference.