Brian Dutton and substitute Charles Ademeno helped Salisbury extend their unbeaten run to 10 league matches.
The Whites squandered several chances before Dutton headed home Sean Clohessy's cross after 70 minutes.
On-loan Southend striker Ademeno returned from a thigh injury to fire a left-footed shot late on.
Eastbourne had earlier seen Sam Gargan's header saved and substitute Simon Wormull shot wide of the left post in first-half stoppage time.
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Salisbury: Bittner, Bass (Davies 84), Ruddick, Brough, Pearce, Clarke, Herring, Dutton, Clohessy, Griffin, Webb (Ademeno 61). Subs Not Used: Porter, Cox, Martin.
Booked: Ruddick.
Goals: Dutton 70, Ademeno 89.
Eastbourne Borough: Hook, Armstrong, Gargan (Wormull 29), Austin, Baker, Pullan, Jenkins, Lovett (Jeffery 77), Brown (Mingle 84), Harding, Tait. Subs Not Used: Jordan, Matt Crabb.
Att: 1,011
Ref: K Yeo (Essex).
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