Home forward Ducros tested Hipkins with a low 20-yard drive in the second minute but the young keeper held it close to his right-hand post.
The Harriers striker won a corner two minutes later and played a short set-piece to Shilton who whipped a low shot into the side-netting from 15 yards.
Foster skilfully volleyed an effort wide from the edge of the area on seven minutes as Harriers continued to call the shots.
Swifts battled their way back into the game but failed to test Brock in the early stages.
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