A goal from Liam Enver-Marum three minutes before the break has given Eastbourne Borough the half-time lead at Priory Lane.
Enver-Marum had twice gone close to breaking the deadlock when he finally scored his eighth goal of the season.
The striker set Joe Benjamin racing away down the right before charging forward to receive the ball back and fire a low shot past Danny Naisbitt from 12 yards.
Benjamin and Enver-Maum had linked well earlier in the game to carve out another opportunity. A bustling run from Benjamin set Enver-Marum up but Gareth Gwillim lunged to block his shot.
Enver-Marum had also been denied by Naisbitt after racing on to a high ball from Kayne McLaggon as Borough ended the half strongly.
Histon, with the help of a strong wind. had been the better team in the early stages with Danny Knowles twice having to save from Bradley Hudson-Odoi from 25 yards.
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