Kneller's 86th minute winner came in a match where United enjoyed the majority of possession but were unable to create many clear cut chances.
Prior to the match there was an impeccably observed minutes silence in memory of lifelong United fan Peter Jones who sadly passed away on Tuesday.
Casey Ham came into the starting XI for his first start, and there were recalls for Chris Agutter and Luke Snashall, who only returned from holiday late on Saturday morning.
It took just three minutes for United to assert their authority on the contest when Shaun Loft rose highest to head past visiting 'keeper Downer.
Despite much of the possession in the first half, United failed to test Downer with Jack Divall going closest when his 18 yard effort went past the post.
United lost Snashall to an ankle injury as half time approached as Patryk Miskiewcz took his place.
The second half began with Storrington looking more lively and in the 52nd minute they drew level when Joe Warner capitalised on a weak header by Peter Featherstone to round Grant Young and place the ball into an empty net.
Minutes later, Warner flashed an effort across the United goalmouth as Storrington began to get hold of the ball and create space.
United were restricted to half chances as Jason Taylor, Wes Tate and substitute Linton Rogers all hit the ball the wrong side of the post. A draw looked likely until Kneller thumped home an unstoppable header past Downer, who was booked in the aftermath for his persistent claims of a foul in the build up to the goal.
United hearts skipped a beat in the final minute of the match as a high ball slipped through the grasp of Young, but Loft was in the right place go clear the ball off the line as United made it 9 points from 9 to move top of SCFL Division Two.
United: Young; Featherstone, Snashall, (Miszkiewcz), Loft (C), Kneller, Divall, Franklin, Tate, Ham (L.Rogers), Taylor