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.
Any reproduction, publication or redistribution of this material without the written agreement of 365 Media Group is strictly forbidden.