GFC found themselves 2-0 down at half-time, having missed a string of chances in front of a bumper crowd.
The visitors scored twice more after the break before Fin Du Port pulled one back from a well-worked corner routine.
But any hope of a comeback was frustrated by the stop-start nature of the second half as Peacehaven used every opportunity to run down the clock on a roasting May afternoon.
More to follow.
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