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It was always going to be a long night for County after Jake Simpson was sent off for a handball on the line after just eight minutes.
Jevons took advantage of that incident to send Matt Glennon the wrong way from the spot and give the Shrimps a perfect start.
Defender Jim Bentley made it 2-0 when he headed home a Craig Stanley corner on 33 minutes from six yards out, before Jevons reacted quickest as Stockport failed to clear a corner three minutes later.
The former Huddersfield striker went close to a third just after the break when his shot was tipped on to the post by Glennon.
But he wasn't denied for long as he completed his treble with a fine finish on 67 minutes, before Scott Brown's deflected effort added the gloss two minutes later.
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