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Danny Adams did equalise for the visitors in the 24th minute to give Stockport some hope, but although substitute Michael Keane missed a penalty, Hull battled on and deservedly took the points.
Hull started the brighter of the two sides and nearly took the lead after only eight minutes. Former Stockport striker Wilbraham, who spent seven years with the Hatters, found space inside the box only to fire wide.
However, Hull were ahead two minutes later and it was Wilbraham who gave them the advantage. He bundled County midfielder Rickie Lambert off the ball and produced a left-footed curler to beat goalkeeper Neil Cutler at the far corner.
Tayor's side continued to press and came close to doubling their advantage in the 18th minute, but midfielder Junior Lewis fired over.
Stockport showed no signs of flagging and kept battling. They were rewarded in their search for an equaliser in the 24th minute. Former Macclesfield Town left-back Adams latched on to a splendid pass from young defender Michael Raynes and found the back of the net with a fierce left-footed strike.
Two minutes into the second half Hull defender Leon Cort was fouled in the box and referee Clive Oliver awarded a penalty. However, with his first touch of the game, substitute Keane failed to convert from the spot as Cutler made a wonderful save diving full stretch to his right.
County, boosted by their keeper's save, nearly took the lead. Striker Warren Feeney chased down a good pass from Lambert and hit the target from the tightest of angles, but left-back Andrew Dawson cleared off the line.
Hull rallied, and in the 61st minute Dawson crossed from the left and Price rose above the County defence to direct a looping header past the helpless Cutler.
And it got even better in the 65th minute for Hull. Wilbraham flicked the ball on from a long ball, Raynes only managed a slight touch trying to head back to Cutler and Allsopp pounced to score with a powerful shot.