Jason Lovell headed in a Terry Cox cross to give Brockenhurst a 20th-minute lead against fellow strugglers Portland United, but that was as good as it got for the beleaguered Badgers.
An overhead kick by the predatory David Laws brought the Dorset side back on terms before the break and he grabbed their winner midway through the second half.
"Individual mistakes have cost us," sighed Brock boss Graham Kemp. "We've huffed and puffed with plenty of effort but had no cutting edge."
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