Donnell McNeilly opened the scoring after half an hour played in the capital for the Blues, reacting the quickest following Dylan Williams' cross into the area.
McNeilly then doubled the hosts advantage in first-half stoppage time, prodding home Zak Sturge's cutback from the byline.
United captain Shola Shoretire scored twice inside six second-half minutes to level the game once more, before Tyrique George's late winner proved pivotal.
Ethan Wheatley was presented with the first opportunity as Travis Binnion's side looked to grab an early foothold in the game.