Jean-Paul Marna scored the decisive goal in the 20th minute to plunge Woking deeper into the Blue Square Premier relegation battle.
Patrice Konan's left-wing cross was flicked on by Alfie Potter and Marna drilled in from 12 yards.
Kettering dominated after Simon Eastwood's early save from Richard Graham's long-range shot.
Woking had few chances - Rob Elvins' near-post header before half time was as close as they came to an equaliser.
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Kettering: Harper, Bennett, Branston, Geohaghan, Luke Potter, Alfie Potter, Boucaud (Wrack 75), Artus (Solkhon 90), Richard Graham, Westcarr, Marna (Beardsley 69). Subs Not Used: Dempster, Jason Lee.
Booked: Beardsley.
Goals: Marna 20.
Att: 1,414
Ref: David Coote (Newark).
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