The fixture was the first time that the sides had met in a competitive fixture and it was the home side that started quicker.
A mistake from Jamie Bunn was pounced on by Wayne Wilkinson, who played in former United striker Paul Rogers who dragged an effort wide of the upright.
Wanderers early perseverance was rewarded with less than ten minutes played as a free kick from another former United player, Simon Catt, was headed in at the far post by Jamie Buckett.
United were indebted to Callum Christie for keeping the deficit at one as he denied Wilkinson from close range.
United’s final ball was far from perfect in the opening half hour, but they pulled level as a deep cross from Ben Farrant was cushioned back into the path of Dom Clarke by Pete Cooper, who proceeded to rifle the ball low and hard into the back of the net.
The lively Seb Saunders saw an effort saved by Joe McLoughlin at the start of the second half as United began to press on, with Clarke also seeing an effort saved by the Wanderers ‘keeper.
With ten minutes left to play and the prospect of extra time looming, United got the goal that would ultimately secure the contest as Liam Baitup showed great awareness when many others had stopped due to Saunders laying prone in the area and placed the ball into the net despite a desperate lunge by McLoughlin.
The goal inspired Wanderers as Callum Christie was forced into two superb acrobatic saves, including a world class stop from a 30 yard drive by Catt.
Wanderers’ task of finding an equaliser in the dying minutes was further hindered when they were reduced to ten men after Adam Byrne was dismissed for a second bookable offence as United held out for victory over their local rivals.
United will now face either Chichester City or Loxwood in the Third Round at The Oval, with the two sides meeting on Tuesday 8th September at Oaklands Park.