As the game entered stoppage time, Town defender Nathan Clarke could only divert Leon McSweeney's powerful goalbound drive past the helpless Alex Smithies.
Terriers' striker Lukaz Jutkiewicz had the ball in the back of the Stockport net inside two minutes, only for a linesman's flag to up for offside.
The visitors had started purposefully and Danny Cadamarteri twice saw shots blocked, then Jim Goodwin's effort was saved by Owain fon Williams.
Stockport had a scare after 13 minutes when they were saved by the woodwork. Town defender Clarke powered in a header that hit the base of a post and bounced behind to safety.
Huddersfield did get their opening goal three minutes later. Jutkiewicz crossed, Cadamarteri laid the ball into Michael Collins' path and he made no mistake with an angled shot from 12 yards.
Stockport old boy Anthony Pilkington came close just before the half-hour mark when his goalbound strike from 20 yards was blocked by Matty Mainwaring.
Jutkiewicz then saw a fancy overhead kick saved by fon Williams.
Tommy Rowe screwed a decent chance wide for the hosts, before a Leon McSweeney drive was bundled round the post by Town keeper Smithies.
The first half-chance of the second period saw Town's Gary Roberts volley well wide from an acute angle.
On the hour mark Stockport's Chris O'Grady stung the palms of Smithies with a powerful shot from the edge of the box, but Huddersfield quickly responded with Pilkington firing inches past the post.
An end-to-end clash then saw Smithies tested again, this time by lively substitute Oli Johnson.
Lionel Ainsworth almost had an immediate impact after coming on as a substitute for the Terriers, but he smashed narrowly wide with fon Williams well beaten.