The win owed something to a moment of controversy when James McArthur appeared to handle the second goal into the back of the net, after Mark McLaughlin's header had looped over keeper Lukasz Zaluska.
It was undoubtedly a turning point, but was probably a break Hamilton deserved after having worked so hard, particularly in the first half.
Yet Dundee United had taken an unlikely lead in 23 minutes when Willo Flood's cross from the left was headed into the bottom left corner by luckless McLaughlin.
That lead lasted only six minutes, however, when free-kick specialist Tony Stevenson drilled a set-piece through the defensive wall and past startled Zaluska.
Accies grabbed their second goal 10 minutes later when McArthur bundled McLaughlin's header into the net.
United tried to get themselves back into the match, but were hit with a classic sucker-punch when McArthur's pass found the lively Richard Offiong in the box and his path was blocked, only for the ball to fall to David Graham, who took a touch before blasting the ball past Zaluska from 16 yards.
Hamilton then had keeper Tomas Cerny to thank for keeping them in front, with a string of superb saves, most notably from Morgaro Gomis and sub Francisco Sandaza.
Sandaza met a Danny Swanson cross with a deft header, which Cerny brilliantly touched past the bottom left corner, before Gomis' netbound effort was punched over the top left corner.
However Accies sub Lucas Akins looked lively throughout and was desperately unlucky to see Zaluska save his fierce effort on the turn in second-half stoppage time.
For an established SPL side with designs on challenging for Europe, this was perhaps a timely wake-up call for United, as Hamilton looked the better and more hungry side throughout.
Graham was unlucky to see an early effort punched away from the top left corner, and Offiong was unfortunate to see a low effort touched onto the base of the right post, having mugged Lee Wilkie of possession.
However, for Hamilton this was an ideal start and one their fans in the 4385 crowd were delighted with, as they face their second test up at Inverness on Saturday.