Daniel Nkrumah struck twice after the break to earn the Beavers a victory and deny Dom Di Paola’s side the chance to build on their midweek win over Bath City.
A largely uneventful first half gave way to home dominance, with Horsham unable to force a comeback.
Horsham are 15th in the table and are on the road again next weekend, to Torquay.
See pictures from the Hampton-Hornets clash – by McCartney Martin – on this page and those linked, and get the latest from the camp on this website and in the West Sussex County Times in the week.
25. Hampton and Richmond Borough v Eastbourne Borough pictures by Lydia and Nick Redman (17).jpg
Eastbourne Borough - seen here in pink - are off to Chippenham for a real six pointer | Picture by Nick Redman Photo: nr
26. Hampton and Richmond Borough v Eastbourne Borough pictures by Lydia and Nick Redman (8).jpg
Borough fans will travel in good numbers to Salisbury | Picture by Lydia Redman Photo: Lydia Redman