Pemi Aderoju’s double propelled Borough to a 2-1 victory at the Southern League Premier Division South outfit.
Aderoju fired the visitors in front on six minutes but Michael Folivi levelled on the stroke of half-time.
Aderoju netted what proved to be the winner from the penalty spot on 72 minutes.
The Sports will welcome National League high-flyers Boreham Wood to the The ReachTV Stadium on Saturday, October 11 for a place in the first round proper.
Borough are back in National League South action this Saturday at Ebbsfleet United.
See some of Lydia Redman’s pictures from the game on this page and the ones linked – and you can read all the latest from Eastbourne Borough in the Eastbourne Herald, out every Friday.
5. FA Cup: Eastbourne Borough edge past Sholing to reach fourth qualifying round - the match in pictures
Eastbourne Borough edged past division-below Sholing to reach the FA Cup fourth qualifying round. Photo: Lydia Redman
6. FA Cup: Eastbourne Borough edge past Sholing to reach fourth qualifying round - the match in pictures
Eastbourne Borough edged past division-below Sholing to reach the FA Cup fourth qualifying round. Photo: Lydia Redman
7. FA Cup: Eastbourne Borough edge past Sholing to reach fourth qualifying round - the match in pictures
Eastbourne Borough edged past division-below Sholing to reach the FA Cup fourth qualifying round. Photo: Lydia Redman
8. FA Cup: Eastbourne Borough edge past Sholing to reach fourth qualifying round - the match in pictures
Eastbourne Borough edged past division-below Sholing to reach the FA Cup fourth qualifying round. Photo: Lydia Redman