Jason Norville turns to celebrate his goal with Dean Sinclair
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Stockport failed to hold off Barnet for a win which would have lifted them away from the League Two danger zone.
Matt Hamshaw gave County the lead when he pounced on Harpal Singh's mis-hit shot to fire home from close range.
The lead lasted for two minutes as Louis Soars' cross was met by Jason Norville, with the ball rebounding off his shin into the net.
Stockport keeper James Spencer kept Barnet at bay, his best save seeing him tip Dean Sinclair's shot over.
Stockport: Spencer, Greenwood, Clare, Raynes, Robinson (Malcolm 79), Hamshaw, Briggs (Wolski 83), Boshell, Singh, Easter, Dje (Bramble 45).
Subs Not Used: Ikeme, Dolan.
Booked: Bramble.
Goals: Hamshaw 15. Barnet: Flitney, Hendon, Yakubu, King, Gross (Charles 66), Bailey, Sinclair, Strevens, Soares, Hatch, Norville (Grazioli 66).
Subs Not Used: Tynan, Lee, Roache.
Booked: King, Hendon.
Goals: Norville 18.
Att: 6,056.
Ref: M Pike (Cumbria).