Torps stooped shortly before half-time to flick home the ball which had been delivered into the danger area by Peter Beagrie from a free-kick on the left wing.
The 44th minute strike was the only goal of the game, and broke the deadlock in a tight game which had seen little goalmouth action.
As well as little goalmouth action, there was little action generally.
United's best chance prior to the goal had fallen to Lee Hodges, but after some desperate defending his shot was blocked.
Stuart Thom thought he had doubled the lead, only for his header to be ruled out by the assistant ref's flag.
Despite the best efforts of the Harriers to get back into the game their fprwards posed little threat for the back line.