The visitors broke the deadlock after 22 minutes when Darren Dods failed to deal with Trent McClenahan's cross and Flavio Paixao made no mistake by finding the top corner from eight yards.
Billy Reid's men doubled their lead on the stroke of half-time when Marco Paixao reacted quickest after his header had been well saved by Dusan Pernis to stab home the rebound.
It was Hamilton's first away win over United since 1989 and ended the Tannadice side's seven-match unbeaten run.
Latvian defender Pavels Mihadjuks was handed his United debut in place of the injured Paul Dixon.
Portuguese striker Flavio Paixao joined his twin brother Marco in the Hamilton side with Trent McClenahan also handed a starting berth.
Hamilton, again without their captain Alex Neil, were dealt another blow when Australian midfielder James Wesolowski injured himself during the warm-up and had to be replaced by Kyle Wilkie.
United created the first opportunity when David Goodwillie linked up with Jon Daly but the Irishman's tame effort was comfortably gathered by Tomas Cerny in the Hamilton goal.
James McArthur had a chance to test Pernis at the other end when he collected Darren Dods' loose clearance but the United captain redeemed himself by blocking the Hamilton midfielder's powerful shot.
Hamilton had only scored once in their previous seven games but Marco Paixao was inches from connecting with an enticing cross from stand-in skipper McArthur as Hamilton looked to break the deadlock.
The visitors did open the scoring when McClenahan's cross fell for Flavio Paixao who shot into the top corner, giving Pernis no chance.
Hamilton could have doubled their advantage four minutes later if Martin Canning had managed to direct his header from Wilkie's cross on target.
The Accies were enjoying the better of the possession and Conway picked up the first booking after 27 minutes for a challenge on McClenahan.
Marco Paixao's corner found Wilkie waiting at the back post and his curling effort had Pernis stranded but failed to dip under the crossbar.
Billy Reid's side did get a second on the stroke of half-time when Flavio Paixao crossed for his brother Marco whose downward header was magnificently saved by Pernis, but the Portuguese striker made no mistake from the rebound.
United manager Peter Houston was clearly disappointed with his side's first-half showing and made a double change at the interval with Damian Casalinuovo and Jennison Myrie-Williams replacing Daly and Conway.
Prince Buaben had an excellent chance to pull a goal back for the Tangerines six minutes after the re-start when he raced onto a cut-back from David Goodwillie but the Ghanaian blasted over from 12 yards.
Houston made his final change, replacing defender Mihadjuks with striker Andis Shala after 58 minutes.
The substitute almost made an immediate impact but Cerny clawed away Shala's glancing header from six yards.
Danny Swanson curled a free-kick over the bar after 67 minutes, after Myrie-Williams had been fouled on the edge of the area by Simon Mensing.
Marco Paixao could have added a third goal for the visitors when he skipped past Sean Dillon's challenge but Pernis managed to push the ball to safety as the Portuguese tried to round him.
United continued to search for a route back into the game but struggled to find a way through a well organised Hamilton rearguard.
When Goodwillie volleyed over the bar in the closing stages the home support knew the visitors would leave Tannadice with all three points.
Hamilton could even have had a penalty in stoppage-time when Garry Kenneth looked to have bundled McClenahan over in the box.