Broughton got his head on another cross on 69 minutes, this time from Joy, but he put the effort into the side netting.Colin Larkin scored the vital winner for Harriers nine minutes from time
York substitute Edmondson should have given them the lead on 73 minutes when he bustled his way through the defence in a robust run only to blaze over the bar from 10 yards.
The home side brought on striker Emmerson for Mathie on 74 minutes.
Three minutes later, Larkin sent Ducros through but his left foot shot was beaten away by keeper Fettis.
And Harrier took the lead on 81 minutes with a goal vital to their play-off hopes.
Ducros' superb lofted through-ball released Larkin who calmly placed the ball past the keeper from 12 yards.
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