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Two late goals by Stefan Payne helped Dover claim a place in the Second Round of the FA Trophy at the expense of non-league football's team of the moment at The Enclosed Ground in East Brighton.
Payne struck after Scott Nielsen's 87th minute free-kick had looked like snatching a replay - but Dover went in front again a minute later with Payne's close range finish, before he put the tie beyond doubt in stoppage-time.
Ricky Modeste robbed a home defender and set-up Payne to score and settle the tie.
A spectacular strike by Nicky Deverdics had put Dover in front 10 minutes into the second half.
Deverdics swung in a corner from the far side, and it flew into the net, past the despairing hand of home goalkeeper and skipper Craig Ross.
Dover struggled in the first half, with Tyrone Sterling and Richard Orlu both forced into last ditch tackles early on.
Ex-Brighton striker Jake Robinson was inches away from putting Hawks in front, the ball going just wide of the far post,
Wide-man Danny Stevens was also very lively - and Sterling was grateful to see the assistant's flag when he left the defender was outpaced on the byline.
Sean Raggett had Dover's first chance after 20 minutes, flicking wide of the near post.
A couple of other Dover attacks came to nothing with Stefan Payne and Miller both struggling to get going.
Miller was booked after a clash with ex-Dover-man Chris Sessegnon, the home defender going down clutching his head.
Whitehawk: Ross, Sessegnon, Braham-Barrett, Mendy, Gotta, Rose, Nielson, Ngamvoloulou, Robinson, Ijaha, Stevens. Subs: Rodrigues, Donaldson, McCauley, Emberson, Hawkins.
Dover: Rafferty, Magri, Raggett, Orlu, Modeste, Miller (Ajala 75mins), Sterling, Deverdics, Parkinson, Thomas, Payne (Murphy 90mins); Subs: Acheampong, Walker.
Ref: Alan Young
Attendance: 392