Banbury dominated the first 30 minutes, Zac McEachran`s effort from 20 yards hitting the outside of the post and City keeper Enol Ordonez making good saves from Ricky Johnson twice and Andy Gunn.
Then, on 32 minutes, against the run of play, City took the lead when a shot from the edge of the area by Joe Carden hit both posts before nestling into the back of the net.
The goal changed the game and United found themselves second best to City until Conor McDonagh's low shot went across Ordonez into the bottom far corner of the net to tie it up at 1-1 at the break.
Although Banbury had the better of the second half they had to wait until the second minute of stoppage time to win it when a mis-kicked clearance from Jack Uttridge found the back of the net.
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