Substitute Marc McGregor scored an 81st-minute goal to ensure Worcester City their first Blue Square South away win of the season.
McGregor headed home a Graham Ward corner to earn the three points that lift City out of the relegation zone.
Basingstoke came close when Worcester's Tom Kemp's attempted clearance came back off the underside of his own bar.
The win takes Richard Dryden's side above Lewes and out of the bottom three in the Blue Square South table.
Worcester City manager Richard Dryden told BBC Hereford and Worcester:
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"I think we got our just desserts today and deserved to win, albeit from a set-play.
"The conditions were hard, especially on one side of the ground and the football wasn't great.
"But we asked for big hearts and commitment like we got against Grays and I think we got that."
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