It was a comfortable win for the Premier League side but Accies can be commended for making a fight of it in the second half.
The home side had threatened to run riot with Jordan Robertson and Morgaro Gomis hitting the frame of the goal early on.
And United went ahead when Barry Robson's deep cross was met at the back post by Hunt who looped a header over Halliwell from an acute angle.
Willo Flood then had a deflected effort from the edge of the box saved by Halliwell before Accies hit back with a James McArthur volley that flew too high.
A Hunt cross found Robson charging in unmarked but his unconvincing header from eight yards went wide of the far post.
The visitors came out in more determined mood after the break but United continued to enjoy the bulk of possession.
United defender Darren Dods headed Robson's corner over the crossbar for the home side's first effort of the second half.
United eventually doubled their lead when Hunt headed past Halliwell from close range from another Robson cross.
United looked to have put the tie beyond doubt but two minutes later their lead was halved.
Accies were awarded a penalty when substitute Brian Wake's cross was handled by Prince Bauben.
Offiong sent Grzegorz Szamotulski the wrong way from the spot to set up a tense finish.
But five minutes from the end Robson again set Hunt up and the Irishman slammed home his hat-trick from six yards out.
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