Cooper cracks winner
Cooper was played through by Scott French, was forced out left but sent a screamer into the top corner of the net from 30 yards.
The match was not without controversy as Town's Greg Manton was sent off for two yellow cards.
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Hide AdAnd a melee involving Hailsham's Nick Barden and East-bourne's Luke Denton saw both escape with yellows.
Hailsham: Tanner, Early, Barden, N Richardson, Reeve, P Richardson, Barnard, Alexander, Leach, Cooper (Mintrum), French.