Richie Foran blasted Inverness into the lead within two minutes of the restart on Sunday before Martin Canning headed home a Brian Easton corner to restore parity after 63 minutes.
But soon after the equaliser Hamilton's James McArthur was shown a straight red card for a tackle on Filipe Morais, which looked to have been a harsh decision on the young midfielder.
Terry Butcher's side failed to take advantage of their numerical advantage despite a late charge and had to settle for a point.
Teenage midfielder James McCarthy was surprisingly named as substitute as the Accies made their third trip to Inverness this season.
Derek Lyle, David Elebert and Derek Asamoah also started for the visitors with full-back Trent McClenahan missing out through injury and on-loan Celtic player Paul McGowan on the bench.
Inverness made one change to the side which defeated St Mirren last weekend with Portuguese playmaker Filipe Morais returning at the expense of Andy Barrowman, who dropped to the bench.
Irishman Foran headed a Morais cross wide inside two minutes but Caley's left-back Lionel Djebi-Zadi was almost punished after being dispossessed by Asamoah.
The lively Ghanaian crossed for Simon Mensing but his effort was blocked before Alex Neil thundered the loose ball over the bar.
Asamoah continued to give Djebi-Zadi a torrid time and Hamilton were presented with a free-kick near the byline when the Frenchman fouled the pacy winger.
Brian Easton flighted the dead ball to Mark McLaughlin at the far post - but Michael Fraser was alert to gather the defender's header.
Inverness should have taken the lead after 19 minutes when Roy McBain crossed for Dougie Imrie but the winger mishit his effort at the vital moment and Foran's subsequent effort was tipped over by Radek Cerny.
Only a fantastic save from Hamilton's Czech goalkeeper prevented Morais giving his side the lead with a powerful first-time volley after 29 minutes.
Hamilton boss Billy Reid was forced to make his first change of the day just after the half-hour mark with McCarthy coming on for the injured McLaughlin.
The visitors enjoyed the better possession as the half drew to a close but struggled to create any real penetration in the final third, although Richard Offiong did flash a free-kick inches wide from 25 yards.
Inverness made a dream start to the second half with Foran running onto a Morais pass before clinically volleying the ball past the helpless Cerny within two minutes of the restart.
The home side were full of confidence and Imrie could have created a second but he elected to shoot weakly into the side-netting instead of finding a better placed team-mate.
Hamilton made their second enforced change of the day when defender Elebert was withdrawn through injury, to be replaced by Chris Swailes.
Foran had the ball in the net for a second time after 56 minutes thanks to a neat finish but the assistant referee had already flagged for offside.
And the home side were to rue that decision when the Accies equalised after 63 minutes.
Canning got the goal, his first of the season, when he rose to head home an accurate Easton corner - despite the best efforts of Ian Black on the line.
But just as Hamilton had found a route back into the game they were reduced to 10 men when McArthur was sent off for a challenge on Morais, which looked to have been a harsh decision on the midfielder.
With less than 10 minutes to go Inverness brought on an extra forward, with Barrowman replacing midfielder McBain.
Offiong should have won the match for the visitors when he raced onto a wonderful pass from Alex Neil but the former Newcastle striker dragged his shot wide.
At the other end, Cerny saved bravely at the feet of Ross Tokely after a well-worked free-kick by Black and Morais.
Inverness continued to press for the winner with David Proctor firing over in the dying stages - but Hamilton held on for a hard-fought point.