Swindon Supermarine end Gosport Borough run
The hosts had the first chance when Harry Williams sent a volley wide of the target.
Alex John was busy for Borough and set up half-chances for Theo Lewis and Marley Ridge.
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Hide AdBoroughkeeper Patrick O'Flaherty then did well to produce two saves in quick succession as Borough came under pressure.
The home side broke the deadlock three minutes before the break, when Borough could only half clear the ball. It fell to Stuart Fleetwood, who hammered in a left-foot volley from 18 yards.
In the second half, Joe Lea went closest on 73 minutes with a shot into the side netting.
Borough then wasted a glorious chance to level in the final minute firing wide from six yards.
Other result: Warminster 3-1 AFC Portchester