Saturday's game was settled when the ball broke off young Celtic defender Eoghan O'Connell after 65 minutes and bobbled into the net at the Caledonian Stadium.
Marley Watkins burst forward down the right flank and sent a superb cross into the box for Billy McKay, but Celtic keeper Lucasz Zaluska took the ball off the striker’s toe only to see it spin off O'Connell.
Celtic, who made 10 changes from the team which drew 1-1 with Maribor in midweek, failed to score in a league fixture for the first time in 59 games.
The game sprung to life on 24 minutes when Kris Commons played a wonderful reverse pass to set up Teemu Pukki inside the penalty area, but Dean Brill twice denied the Celtic striker at his near post.
Three minutes later, Pukki sent Commons clean through and Brill again came to Caledonian Thistle’s rescue to claw away the powerful net-bound shot.
Seconds before that counter-attack, Inverness felt they should have had a penalty when Ryan Christie went down as Filip Twardzik challenged him, but referee Bobby Madden was well placed to judge the incident and waved play on.
Nir Biton then took a pass from Dylan McGeouch at the front of the box and sidestepped a challenge to curl a drive against the crossbar with Brill beaten.
Charlie Mulgrew was well placed under the bar to nod a looping Gary Warren header clear from a Graeme Shinnie corner, with Josh Meekings lurking next to the Celtic skipper.
After the break, Commons sent a lofted pass in front of Leigh Griffiths and although the striker’s shot was on target Brill was well positioned to save.
Five minutes after the opening goal, Commons exchanged passes with substitute Tony Stokes but Brill got down to save the midfielder’s low drive at full stretch.
At the other end, Christie dragged a shot through Mulgrew’s legs and inches wide of the target from the edge of the box.
Nick Ross was denied by Zaluska in the dying minutes after a great counter-attack with the Celtic keeper turning his shot from 12 yards past the post.