Alex D'Acol headed the hosts ahead early on from Ali Crawford's corner.
Inverness had the chance to level after Darian MacKinnon fouled Billy Mckay in the box but Greg Tansey's penalty was saved by Gary Woods.
Grant Gillespie converted Rakish Bingham's pass to double Accies' lead and Bingham added a goal of his own.
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The visitors had been boosted by former striker Mckay's loan signing from Wigan being completed shortly before kick-off to allow him to play, but it was Accies who dominated as they welcomed back the experienced Mikey Devlin and Massimo Donati after injury.
Both sides had been struggling to find a win, and the lack of confidence was evident for most of the first half, although Mckay blasted a volley into the side netting to give the small band of away fans some early hope.
Before the match Hamilton boss Martin Canning had said the first goal would be hugely influential and it was his side who grabbed it with a well rehearsed move from Crawford's corner.
D'Acol got away from his marker on the near post and his glancing header found the net past Owain Fon Williams for his seventh goal of the season.
Caley Thistle then blew a major opportunity to equalise after referee Euan Anderson had pointed to the spot on 26 minutes. Woods guessed right, diving right to produce a superb save to deny Tansey.
Accies then lost Crawford to injury just after the half-hour, with new signing Blair Adams taking his place and Gillespie taking on Crawford's midfield responsibilities.
That move paid off after the interval when Bingham drove down the left, crossed low into the box and Gillespie timed his run superbly to send a side-foot shot past Fon Williams.
Bingham then produced the best moment of the night, smashing a terrific 18-yard effort high past the Welsh goalkeeper for his fourth goal of the campaign, the Caley Thistle defence ripped apart and their fans starting to dread the long, late trip home.
It was a first league win in 12 for Hamilton and only their third in the division this season. Meanwhile, Richie Foran has a major task ahead to convince his men that they can stay in a top flight becoming tougher and tougher as Inverness' winless league run stretched to the dozen mark.
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Hamilton player-manager Martin Canning: "The performance was similar to Saturday, but there were key moments there with the penalty save and the second goal, because we have not been taking the opportunity to get the second goal when we have had the chance so far this season.
"If we continue to make the big moments go in our favour and capitalise on them, then we can move up the table and continue to win games.
"We haven't punished teams, but tonight we did and we make it comfortable for ourselves and that should have probably happened four or five times this season.
"The league is so tight, we have gone from joint bottom to four points off the top six and it gives us a great incentive to go on and try to do something against Kilmarnock on Saturday."
Inverness manager Richie Foran: "That puts us into a relegation battle now - forget about top six, we are in a relegation battle now.
"Some of our players have not got the bottle, they showed that today. We might have been the better side in the first half and their keeper pulled off a great save from the penalty, but some of our boys are hiding and we are in for a fight now.
"I told them straight, 'I can see who is bottling it, I can see who does not want to take the ball'. It is not them all - I thought Billy Mckay was excellent - but it makes it a massive game for us now on Saturday against Dundee.
"That was our worst defeat of the season. I'll take my share of the blame, but the players now need to stand up and be counted."
Match ends, Hamilton Academical 3, Inverness CT 0.
Second Half ends, Hamilton Academical 3, Inverness CT 0.
Attempt missed. Liam Polworth (Inverness CT) left footed shot from outside the box is high and wide to the left.
Massimo Donati (Hamilton Academical) wins a free kick in the attacking half.
Foul by Dean Ebbe (Inverness CT).
Foul by Blair Adams (Hamilton Academical).
Larnell Cole (Inverness CT) wins a free kick in the defensive half.
Attempt missed. Grant Gillespie (Hamilton Academical) left footed shot from the centre of the box is close, but misses to the left.
Corner,  Hamilton Academical. Conceded by Brad McKay.
Foul by Dougie Imrie (Hamilton Academical).
Liam Polworth (Inverness CT) wins a free kick in the attacking half.
Attempt missed. Blair Adams (Hamilton Academical) header from the right side of the box is close, but misses to the right.
Attempt missed. Blair Adams (Hamilton Academical) header from a difficult angle on the right is close, but misses to the right.
Substitution, Hamilton Academical. Eamonn Brophy replaces Alejandro D'Acol.
Corner,  Inverness CT. Conceded by Scott McMann.
Substitution, Inverness CT. Dean Ebbe replaces Henri Anier.
Attempt missed. Michael Devlin (Hamilton Academical) header from the centre of the box is close, but misses to the left.
Corner,  Hamilton Academical. Conceded by David Raven.
Substitution, Hamilton Academical. Steven Boyd replaces Rakish Bingham.
Attempt saved. Larnell Cole (Inverness CT) right footed shot from outside the box is saved in the top right corner.
Corner,  Hamilton Academical. Conceded by Gary Warren.
Attempt saved. Liam Polworth (Inverness CT) right footed shot from the right side of the box is saved in the centre of the goal.
Goal!  Hamilton Academical 3, Inverness CT 0. Rakish Bingham (Hamilton Academical) right footed shot from outside the box to the top right corner. Assisted by Darian MacKinnon.
Alejandro D'Acol (Hamilton Academical) wins a free kick in the defensive half.
Foul by Brad McKay (Inverness CT).
Substitution, Inverness CT. Larnell Cole replaces Ross Draper.
Massimo Donati (Hamilton Academical) wins a free kick in the attacking half.
Foul by Henri Anier (Inverness CT).
Attempt blocked. Liam Polworth (Inverness CT) right footed shot from outside the box is blocked.
Attempt blocked. Henri Anier (Inverness CT) right footed shot from outside the box is blocked.
Darian MacKinnon (Hamilton Academical) is shown the yellow card for a bad foul.
Foul by Darian MacKinnon (Hamilton Academical).
(Inverness CT) wins a free kick in the attacking half.
Corner,  Hamilton Academical. Conceded by David Raven.
Attempt saved. Billy McKay (Inverness CT) header from the centre of the box is saved in the top centre of the goal.
Attempt missed. Blair Adams (Hamilton Academical) left footed shot from outside the box is close, but misses the top left corner.
Goal!  Hamilton Academical 2, Inverness CT 0. Grant Gillespie (Hamilton Academical) right footed shot from the centre of the box to the bottom right corner. Assisted by Rakish Bingham.
Attempt saved. Liam Polworth (Inverness CT) right footed shot from outside the box is saved in the centre of the goal.
Second Half begins Hamilton Academical 1, Inverness CT 0.
First Half ends, Hamilton Academical 1, Inverness CT 0.
Hamilton Academical moved three points clear of Premiership bottom side Inverness Caledonian Thistle with victory over the Highlanders.