The Southern League premier south division side won 2-0 to increase the pressure on Mark Beard and his team, who have also been struggling in their National League South campaign.
Borough look for an upturn when they go to Dover on Tuesday night.
See pictures from Hendon v Eastbourne Borough by Lydia and Nick Redman on this page and the ones linked – and get the Borough latest in the Herald, every Friday.
37. Hendon v Eastbourne Borough FA Trophy pictures by Lydia and Nick Redman (1).jpg
Hendon v Eastbourne Borough in the FA Trophy Photo: Nick Redman:Nick and Lydia Redman
38. Hendon v Eastbourne Borough FA Trophy pictures by Lydia and Nick Redman (29).jpg
Hendon v Eastbourne Borough in the FA Trophy Photo: Lydia Redman:Nick and Lydia Redman
39. Hendon v Eastbourne Borough FA Trophy pictures by Lydia and Nick Redman (33).jpg
Hendon v Eastbourne Borough in the FA Trophy Photo: Lydia Redman:Nick and Lydia Redman
40. Hendon v Eastbourne Borough FA Trophy pictures by Lydia and Nick Redman (36).jpg
Hendon v Eastbourne Borough in the FA Trophy Photo: Lydia Redman:Nick and Lydia Redman