Borough had struggled for a breakthrough until two fine finishes by Harrison – his first goals for the Sports – saw the Rams raised.
Borough will aim to keep their fine run going on Tuesday night when they are at home to 21st-placed Stanway Rovers.
See pictures from Eastbourne Borough 2 Ramsgate 0 on this page and the ones linked. Get the latest from Priory Lane in the Eastbourne Herald every Friday.
25. Eastbourne Borough v Ramsgate pictures by Lydia and Nick Redman (56).jpg
Eastbourne Borough v Ramsgate, Isthmian Premier Photo: Lydia Redman : Lydia and Nick Redman
26. Eastbourne Borough v Ramsgate pictures by Lydia and Nick Redman (62).jpg
Eastbourne Borough v Ramsgate, Isthmian Premier Photo: Lydia Redman : Lydia and Nick Redman
27. Lydia Redman
Eastbourne Borough v Ramsgate, Isthmian Premier Photo: Lydia Redman : Lydia and Nick Redman
28. Lydia Redman
Eastbourne Borough v Ramsgate, Isthmian Premier Photo: Lydia Redman : Lydia and Nick Redman