In a first half where for the majority chances were in short supply, Caley Thistle will feel they should have been at least one in front going in at the interval.
Richard Hastings so nearly made himself an unlikely goalscorer with an effort that was only a yard away from finding the top corner, after collecting Ross Tokely's cross at the back post.
Celtic's only opportunity of any note came from Aiden McGeady forcing Michael Fraser into a smart save at his near post. From the resultant corner, Barry Robson almost picked out Gary Caldwell, but he could not force his header home from close range.
It was Inverness, however, who twice came close to opening the scoring. Firstly, a Dougie Imrie free-kick from 25 yards was only half a yard over the crossbar, before Garry Wood passed up the chance of the game.
The young striker worked a neat one-two with the impressive Don Cowie, but from eight yards out his low shot was saved by the outstretched leg of Artur Boruc.
Failure to convert your chances against the likes of Celtic is usually punished, however and only three minutes into the second half the visitors took the lead.
Lee Naylor's low cross found the unmarked Scott Brown in the middle and he had all the time in the world to guide the ball home from six yards.
Celtic were now beginning to find some form and went further in front on 65 minutes, Robson's cross finding the head of Glenn Loovens who made no mistake with a powerful header.
But Inverness gave themselves hope four minutes later, Wood bundling the ball home after substitute Adam Rooney had failed to properly connect with Tokely's cross.
Despite some late pressure from Caley Thistle, which included five minutes of injury-time, Celtic held out for a valuable three points to maintain their lead at the top of the table.