The win puts Accies six points clear of their Highland rivals, while the Lanarkshire side also moved five points ahead of Falkirk, courtesy of the Bairns' defeat at Ibrox.
Hamilton were deserved winners over the piece and although Inverness rallied in the second half, they will be disappointed not to have posed more of a threat.
Inverness survived a few penalty claims early in the game. First Paul McGowan's cross from the right struck Richard Hastings' hand, although the Caley defender couldn't do much to get out of the road.
Then James McCarthy was tripped in the box by Don Cowie, which looked like a stick-on penalty, but referee Brian Winter wasn't interested.
In between those claims Inverness had their best chance of the game, when Ross Tokely cut inside from the right channel and sent a delicate chip inches over the top left corner after 11 minutes.
But after 38 minutes Hamilton striker Joel Thomas darted into the box, only to be brought down by a clumsy challenge from Grant Munro and this time Mr Winter pointed to the spot.
Mensing stepped up and confidently rammed the spot-kick high past Ryan Esson.
Conditions worsened at half-time, with freezing rain lashing the pitch for the duration.
Inverness came out for the second half with their tails up and they should have levelled in 57 minutes, when Roy McBain's cross from the right seemed perfect for sub Garry Wood.
But he didn't connect solidly enough with a back-post header and the chance was lost.
Hamilton passed up a good chance after 61 minutes when Brian Easton went on a roving run down the left before picking out Paul McGowan, but the striker's dipping shot landed behind Esson's goal.
Caley went close again in 63 minutes when Cowie found Filipe Morais and the Hibs loan star's first-time effort was just inches over the top right corner with Tomas Cerny scrambling.
A free-kick on the right corner of the box then gave Thistle another opening, but although Iain Vigurs was only inches over in 67 minutes, Cerny seemed to have it covered.
Sub Dougie Imrie saw a free-kick blocked by Cerny's chest in 78 minutes, with Chris Swailes hacking clear.
Morais had one last chance in 83 minutes when he saw a curling effort punched over by Cerny, but Hamilton held on for their fourth successive home win, consigning Inverness to a seventh straight defeat - their worst record in 15 years.