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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 net 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 equalize after referee Euan Anderson pointed to the spot after 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 defense was ripped apart, and their fans were starting to dread the long, late trip home.
It was a first league win in 12 for Hamilton and only their third in...

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Hamilton Academical hat sich mit dem Sieg über die Highlanders drei Punkte vor dem Premiership-Schlusslicht Inverness Caledonian Thistle durchgesetzt.<end_of_turn><eos>