Burnley began brightly and almost had the benefit of an early goal as Wade Elliott surged down the middle of the United defence, cut inside on to his left foot and struck the woodwork with his shot from the edge of the box.
Midfielder Chris McCann then headed over at the far post following a cross by left-back Christian Kalvenes.
At the other end Clarets goalkeeper Brian Jensen was fortunate to push a Greg Halford free-kick behind for a corner.
United manager Kevin Blackwell replaced left-back Gary Naysmith after the defender received a torrid time from Burnley winger Chris Eagles.
The only goal of the game arrived midway through the first half when a Rhys Williams cross was glanced home by the head of Paterson.
Stephen Quinn had a good opportunity following a free-kick from Matthew Kilgallon but the midfielder fired over from the edge of the penalty area.
Visiting striker Craig Beattie was too slow to get in a shot when well placed, while Darius Henderson did manage a fine volley which Jensen tipped over the crossbar.
Elliott brought a save out of Paddy Kenny early in the second half and the keeper excelled on 51 minutes to keep out a shot from McCann after Robbie Blake had danced his way up the byline.
Henderson missed the target just before the hour mark after the Burnley defence failed to clear another Halford free-kick.
A swift Burnley counter-attack led by McCann enabled Blake to once again test Kenny while substitute Jamie Ward had a shot held on his near post by Jensen.
Not even the addition of five minutes of stoppage time by referee Graham Laws could prevent the home side from collecting three precious points.