The visitors, with coach Steve Ferguson in charge following the sacking of Derek Adams as boss earlier in the week, held firm for the opening 45 minutes as they went in search of their first points of the season.
However, they crumbled after the break with Martin Canning opening the scoring for the Accies in the 47th minute.
Mickael Antoine-Curier then netted twice from the penalty spot before Jason Scotland sealed Hamilton’s fourth win of the season in injury-time.
Hamilton went close early on as Dougie Imrie teed up a shot for Ziggy Gordon but he drilled inches wide of the post.
Tony Andreu then screwed an effort just over the crossbar from Grant Gillespie’s cutback following some impressive play from the home side.
Accies still looked more likely to find the back of the net and Antoine-Curier went down in the box under pressure from Uros Celcer but there was no penalty award from referee Willie Collum.
Darian MacKinnon then stabbed into the path of Antoine-Curier but the ball came to him too quickly and he fired straight at goalkeeper Mark Brown, who was able to save the point-blank shot.
The first half ended goalless but the match sparked into life in the second half as Accies surged into the lead two minutes after the restart.
Danny Redmond whipped a corner into the box where Canning was waiting to nod home at the back post.
The referee then pointed to the penalty spot with 57 minutes on the clock when Andreu was felled in the box by Rocco Quinn, and Antoine-Curier stepped up to convert from 12 yards.
The home side increased their lead further five minutes later with their second spot-kick of the day.
This time Celcer was deemed to have denied Imrie a clear goalscoring opportunity and was shown a straight red card before Antoine-Curier again hit the target.
Incredibly, Collum handed out a third penalty – this time to County – after 67 minutes for what looked like a coming together between Gordon and Liam Boyce.
But hopes of County hauling themselves back into the game were shattered when Richie Brittain was denied by goalkeeper Michael McGovern, and Joe Cardle’s rebound was hooked to safety by Mikey Devlin.
Scotland then put the gloss on the win for Accies when he met a cutback from Louis Longridge and produced a nice finish to add his name to the scoresheet in injury time.