After several near misses the Ducks eventually opended their account in the 37th minute when Billy Holmes sent a 25 yarder in off the far post with Dorchester keeper Bob Brittain groping for thin air.
Dorchester player manager Martin Chivers (ex Spurs and England striker) almost equalised right on half time when his shot from inside the box was heading for the bottom corner till Ducks keeper Keoth Baker got down to save superbly.
Holmes thundered a shot against the bar early in the second half and after Barrie Thomas, Peter Poore and Hedley Steele all had brief openings for the visitors, United sealed their win in the 88th minute when John Bailey fired home following a corner.