Kai Corbett opened the scoring after three minutes and Liam Nash doubled the lead shortly before the break. Josh Rees added a third late in the game.
It was just what Steve King’s side needed after three straight league defeats and lifted them up to 12th in the table.
The Sports are at home again on Tuesday, when Chatham Town visit.
See pictures by Lydia and Nick Redman from Eastbourne Borough 3 Cheshunt 0 on this page and those linked and get the local football action in the Eastbourne Herald every Friday.
49. Eastbourne Borough v Cheshunt pictures by Lydia and Nick Redman (6).jpg
Eastbourne Borough v Cheshunt, Isthmian Premier Division Photo: Lydia Redman : Lydia and Nick Redman
50. Eastbourne Borough v Cheshunt pictures by Lydia and Nick Redman (8).jpg
Eastbourne Borough v Cheshunt, Isthmian Premier Division Photo: Lydia Redman : Lydia and Nick Redman
51. Eastbourne Borough v Cheshunt pictures by Lydia and Nick Redman (2).jpg
Eastbourne Borough v Cheshunt, Isthmian Premier Division Photo: Lydia Redman : Lydia and Nick Redman
52. Eastbourne Borough v Cheshunt pictures by Lydia and Nick Redman (5).jpg
Eastbourne Borough v Cheshunt, Isthmian Premier Division Photo: Lydia Redman : Lydia and Nick Redman