A brace from Warren Feeney and a third goal from youngster Ashley Williams ensured a comfortable passage into the FA Cup second round for Stockport League One basement side County made five changes in a bid to arrest a worrying losing sequence, but it was the visitors who were first to show when Anthony Lloyd let fly from distance but his shot curled just past the post.
The home side did get the early fillip they were after, however, when Ashley Williams powered home a header on eight minutes from skipper Danny Griffin's corner.
The Terriers responded with another shot from Lloyd which was well saved by County goalkeeper James Spencer, but on 20 minutes debutant Andy Smith picked out Feeney and his fellow Northern Irishman smashed home to make it 2-0 to Sammy McIlroy's side.
Chris Brandon volleyed inches over for Huddersfield as they tried to regain some momentum, but Feeney again went close for Stockport just beyond the half-hour when his shot flew just wide.
For the first time in a while County were cruising, and on 38 minutes young striker Chris Williams fired in a curling shot which visiting goalkeeper Paul Rachubka plucked out of the air well.
Amazingly Stockport stretched their lead still further on the stroke of half-time when Feeney made the most of an Andy Holdsworth slip and poked the ball home from close range.
Pawel Abbott missed a great early second-half chance for Huddersfield when he volleyed agonisingly over on 47 minutes, then just beyond the hour mark Junior Mendes was only denied by a goalline clearance from John Hardiker.
Abbott did make it 3-1 in the dying seconds with a neat finish from 12 yards.