The teams went in goalless at the break after the visitors started the match brightly, winning a series of corners just after the quarter-hour mark that ended with a free kick in a dangerous position, Virgil van Dijk fouling Marley Watkins.
Greg Tansey's free kick was stopped by the returning Lukasz Zaluska, and neither side could offer a meaningful effort before the break, half-hearted attempts from Mubarak Wakaso and Anthony Stokes not enough to break the deadlock.
The breakthrough came after the restart when John Guidetti, on loan from Manchester City, was fed by Anthony Stokes and found the back of the net when he smashed the ball high and hard into the Inverness goal.
Adam Matthews replaced Mikael Lustig on the hour as the visitors continued to be a thorn in Celtic's side, Marley Williams and Greg Tansey both putting the ball over the bar after good work from Inverness.
Billy McKay, scorer of the only goal when the two sides last met in the league, was introduced with 20 minutes remaining, though his eagerness to get his side back into the game ended in him being pulled up for a series of fouls.
Despite their best efforts, Inverness did not test the Celtic goal as much as they could have and now find themselves in fourth with Ronny Deila's side moving up to second.