Most of the first-half pressure came from the Accies at New Douglas Park, including a left-footed shot from outside the box by left-back Stephen Hendrie which was saved in the bottom corner in the 21st minute.
Team-mate Tony Andreu forced a similar save ten minutes later.
Kilmarnock came out battling in the second half and striker Josh Magennis first had a right-foot shot saved and then went just wide with a header.
But Hamilton stepped up as they sought the win that would have kept them top and Ali Crawford’s 67th minute shot from close range forced a save.
Hendrie then nearly settled it in the 90th minute when he went close with a left-footed strike from just outside the box.
Two minutes later Crawford hit a shot from outside the box which again forced a save but it was not enough to prevent Inverness leapfrogging them to take top spot in the table thanks to their 2-1 victory over St Johnstone.