The strong wind did little to help either side, with free flowing football at a premium throughout the contest as both sides struggled with the elements.
The first half saw United try to take what little advantage there was from the conditions, by shooting at the home goal when the opportunity arose.
Liam Painter saw a 25yd effort comfortably gathered by home stopper Fraser Trigwell inside the opening minute, while Peter Featherstone saw an audacious 35 effort just clear the crossbar.
Trigwell made a smart stop to deny Peter Cooper with ten minutes played after the United striker had turned his marker on the edge of the area before unleashing a shot that was tipped onto the frame of the goal.
Worthing began to grow into the game and had a ten minute spell where they applied some pressure to the United defence, with Pat Rose coming close with an overhead kick that James Broadbent parried behind for a corner before Paul Elliott found himself one on one with Broadbent but the striker pushed the ball wide of goal under pressure from the tracking Dean Stevens.
Stevens was next to try his luck for United as he saw two efforts saved by Trigwell as the first half came to a close.
The second half became a lot scrappier, with neither side retaining possession and failing to stamp their authority on the contest.
The decisive goal in the contest came with eleven minutes left to play as Dave Smart’s free kick was parried by Trigwell and following a brief scramble inside the six yard box the ball fell to Bunn and United’s utility man stabbed the ball into the net to the clear relief of the visitors