Accies had gone over nine hours without a goal but, after a turgid start to the match, they opened the scoring from a free-kick out of keeping with the match up to that point.
Richie Foran's foul on Simon Mensing gave the visitors a set-piece 25 yards out. With everyone expecting a shot at goal, Alex Neil played the ball to the unmarked James Gibson just inside the area and he took a touch before lashing a shot low past Ryan Esson and into the corner.
Caley Thistle's response was muted. Ian Black had the best effort as he worked space on the edge of the box only to drag a weak shot wide.
In stark contrast, Hamilton were looking far more dangerous and might have gone even further in front after 34 minutes.
Joel Thomas' header was hooked on by James McCarthy into the path of Paul McGowan, but the on-loan Celtic forward was superbly denied by Esson on the edge of his own area.
Accies continued to push for a second and, four minutes before the interval, Mensing hit a speculative effort from 22 yards that had to be gathered at the second attempt by Esson with McGowan waiting to pounce.
Inverness had rarely been seen as an attacking threat, but they may have gone in at half-time all-square had Filipe Morais not sent his lob narrowly over the crossbar having done well to run on to a Foran pass.
The Portuguese-born forward then attempted to make amends for this miss six minutes into the second half, testing Tomas Cerny with a low shot that the keeper had to save at his near post.
Morais then turned creator on 62 minutes, his cross picking out the unmarked Dougie Imrie who somehow headed wide from six yards out.
Ten minutes later, Morais whipped in another dangerous ball that Cerny punched away only as far as Black, but his looping header dropped on to the roof of the net.
In their desperate bid to get an equaliser, Caley Thistle pushed Ross Tokely forward and he was instrumental in setting up Kerr for a late leveller. His volley from the edge of the box took a slight deflection as it bounced past the wrong-footed Cerny three minutes from time to earn the Highland Capital side a much-needed point.