Accies made United work for the win, pushing their SPL rivals close up until the later stages of the game.
United dominated the first half and Jordan Robertson nearly scored after just two minutes, cutting in from the left before unleashing a powerful drive that Bryn Halliwell did well to hold at the near post.
Morgaro Gomis sent a 20-yard drive crashing off the bar nine minutes in after Barry Robson's cross was only partially cleared.
United's captain then picked out Noel Hunt on the left a minute later and he made it look easy as he looped a header over Halliwell and into the bottom right corner.
Hamilton weren't without their chances but Mark Gilhaney hooked his shot well over from a Richard Offiong cross with quarter of an hour gone.
The underdogs could have leveled after 28 minutes when Gilhaney picked out James McArthur just outside the box but his shot was off target.
Then as the half came to a close, United's keeper Grzegorz Szamotulski had to punch clear after Offiong rifled in a stinging shot on the turn.
Hamilton looked much more comfortable in the second half but despite having decent periods of possession they couldn't find many inroads.
However United's Willo Flood was fortunate to escape Referee Mike McCurry's wrath when he appeared to handle in the box.
United scored their second in 77 minutes when Christian Kalvenes played Robson down the left and his cross was headed in by Hunt.
Hamilton pulled a goal back when substitute Brian Wake's cross was handled in the box by Prince Bauben and Offiong scored from the spot.
However Robson and Hunt combined again in 85 minutes, when the latter sealed his hat-trick with a neat side-footed finish.