Already-relegated Eastbourne beat Bath to pick up their first win in five.
Steve Brinkhurst flashed an effort wide for the hosts early on, while City's Gethin Jones saw an effort well-saved by Rikki Banks.
The Sports took the lead after the break when Richard Pacquette slammed home Danny Kelly's cross.
Pacquette then struck the crossbar but the home side were not to be denied as Mickey Demetriou played in Jamie Taylor to slot in from 12 yards.
Eastbourne Borough: Banks, Austin, Elphick, Kelly, Demetriou, Brinkhurst, Johnson, Hutchinson, Matt Crabb (Jenkins 90), Pacquette (Purcell 85), Taylor (Smart 89). Subs Not Used: Lightwood, Nathan Crabb.
Goals: Pacquette 46, Taylor 83.
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Bath City: Borhy, Simpson, Jones, Webb, Henry (Clough 50), Jombati (Mackie 68), Rollo, Canham (Burnell 77), Hogg, Connolly, Phillips. Subs Not Used: Robinson, Egan.
Att: 1,014
Ref: T Robinson (England).
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