Accies went into the game looking to make it 13th time lucky having failed to pick up a win in the 12 games since Alex Neil left to take up the hotseat at Norwich.
However, despite dominating for long spells in the game and creating a number of chances, a Chris Erskine sucker punch with 20 minutes remaining ensured they left Dundee with nothing.
United had goalkeeper Radoslaw Cierzniak to thank for keeping them in the game at times, as he produced a number of good saves, especially in the second half, to deny the visitors and ensure that United won their first game in 10.
Hamilton had the better of the early possession with Cierzniak keeping out Louis Longridge before Charlie Telfer blasted a free kick over the bar for United.
Ali Crawford and Longridge had half-chances for the away side who also went close on the half hour mark when Crawford’s corner was flicked on by Michael Devlin to Nigel Hasselbaink, whose shot was cleared off the line by Paton.
United striker Nadir Ciftci then had a couple of opportunities before the break, firing wide from 20 yards before forcing Michael McGovern into a save after shooting on the turn.
Hamilton looked lively after the restart, and Stephen Hendrie came closest to breaking the deadlock as his effort beat Cierzniak but crashed off the post.
Accies had a shout for a penalty when Darian MacKinnon’s effort appeared to be blocked by a Dundee United arm in the box but referee Andrew Dallas waved away the protests.
The home side had Cierzniak to thank for keeping them in the game as Hamilton carved out a number of chances – the Polish ‘keeper kept out efforts from Longridge and substitute Jason Scotland before denying Crawford twice, first tipping a free kick on to the woodwork and then turning another effort round the post.
But it was United who then took the lead against the run of play after 70 minutes when Erskine carved out a bit of space before firing an effort past McGovern from 12 yards.
That seemed to take the sting out of Hamilton’s attacking play and it could have ended 2-0 to the hosts when Ciftci set up Mario Bilate at the back post, but the substitute somehow prodded the ball past the post with the goal gaping.