The striker netted the only goal of a close encounter in first-half stoppage-time as Accies held on to top spot with a second straight victory since promotion.
Caley Thistle new boy Adam Rooney was impressive after he came on at half-time but he could not find an equaliser.
Ross Tokely started as skipper for Inverness and Grant Munro missed out with a knee injury, while Hamilton named the same starting XI who defeated Dundee United on Monday.
In a first half where goalscoring chances were few and far between, it was the home side who had the first chance of the game when Douglas Imrie's cross eventually fell to Roy McBain, whose volley was well saved by Tomas Cerny.
Hamilton started to ask questions of the Caley defence when a searching ball from Anthony Stevenson found Offiong but his effort was blocked by Philip McGuire.
Andrew Barrowman was released by Ian Black after 12 minutes but Cerny rushed out to clear the danger, with referee Stevie O'Reilly waving away the forward's appeals that the keeper had handled outside the box.
Hamilton started to take the initiative and Mark McLaughlin was unlucky to see his header go over Michael Fraser's bar when he was first to a Stevenson corner.
Inverness were struggling to break down a stubborn visiting defence.
McBain had a chance when he headed a Richard Hastings cross goalward but his effort went over the bar.
After 34 minutes, James McArthur found time and space beyond the Caley defence but his tantalising ball found no takers.
Four minutes later, Hamilton had the best chance of the game thus far. A Stevenson header was won in the air by Simon Mensing, who knocked the ball onto Offiong but the striker failed to keep his header under the bar.
Two minutes before the break, Don Cowie exploded onto a Barrowman knockdown before being brought down by McArthur. Cowie took the free-kick himself but his effort curled harmlessly over Cerny's bar.
It was the away side who eventually made the breakthrough when Offiong got the better of debutant Jamie Duff and kept his composure to pass the ball beyond the helpless Fraser.
Rooney came on at half-time for Russell Duncan, while Imrie and Cowie switched flanks as home boss Craig Brewster looked to get Inverness back on level terms.
Rooney almost made an immediate impact when he found a way past the Hamilton defence to fire across the six-yard box but his pass found no takers.
After 54 minutes, Hamilton's Alex Neil was booked for a crunching challenge on Imrie as Caley began to take control of the match.
They should have got back level when Cowie found himself with time and space in the box but his woeful effort was easily cleared.
Accies boss Billy Reid brought on Lucas Atkins and Mark Corcoran for Offiong and David Graham as the away side tried to maintain their advantage.
And Hamilton did begin to dominate again with Stevenson producing several fine deliveries into the Caley box but Atkins and Corcoran could not get on the end of them.
Barry Wilson came on for Cowie after 71 minutes and the Inverness veteran was immediately involved when he won a free-kick from Brian Easton.
Imrie's delivery was well punched away by Cerny under pressure.
Brewster had one last throw of the dice when he put striker Rory McAllister on for Duff.
The writing was on the wall for Caley when Tokely could only head a Wilson corner into the stand.
Corcoran had a chance to wrap up the points but he pulled his effort wide. The substitute was denied minutes later when he was quickest to react to Fraser's stop from a Mensing shot but his effort was saved, although he was adjudged to be offside in any case.
McAllister sneaked in behind Stevenson but headed his effort harmlessly wide with only three minutes remaining.
Cerny was booked for time wasting late on but Hamilton's dogged defence managed to hang on for all three points.