The Sports had Elliott Johnson sent off early in the second half – harshly so, according to boss Steve King – and went close to nabbing a late winner themselves before Kofi Anokye-Boadi pounced for a Tanners winner in the 86th minute.
It leaves them in mid-table after what’s now a mixed start to life at step three.
They look to put it right with a visit to one of King’s former clubs, Lewes, on bank holiday monday.
See pictures from Eastbourne Boro 0 Leatherhead 1 on this page and those linked – and get all the latest from Priory Lane in the Eastbourne Herald, out on Friday.
41. Eastbourne Borough v Leatherhead pictures by Lydia and Nick Redman (28).jpg
Eastbourne Borough v Leatherhead, Isthmian Premier Photo: Lydia Redman : Lydia and Nick Redman
42. Eastbourne Borough v Leatherhead pictures by Lydia and Nick Redman (10).jpg
Eastbourne Borough v Leatherhead, Isthmian Premier Photo: Lydia and Nick Redman
43. Eastbourne Borough v Leatherhead pictures by Lydia and Nick Redman (9).jpg
Eastbourne Borough v Leatherhead, Isthmian Premier Photo: Lydia and Nick Redman
44. Eastbourne Borough v Leatherhead pictures by Lydia and Nick Redman (3).jpg
Eastbourne Borough v Leatherhead, Isthmian Premier Photo: Lydia and Nick Redman