Rowe breached what looked in pre-season to be a formidable back-line, boasting experienced defenders Chris Lucketti and David Unsworth, in first-half stoppage time.
The Town defence had been untroubled until then but they allowed Johnny Mullins to cross from the right and Rowe, unmarked, side-footed home.
Huddersfield's new boss Stan Ternent fielded six of his seven new signings and one of them - winger Gary Roberts - ran the show for the home side.
Roberts, a £250,000 recruit from Ipswich, provided a big threat from set-pieces in particular.
Veteran striker Andy Booth gave Huddersfield the lead on the half-hour when he jumped between two defenders to head home Roberts' corner.
Huddersfield should have gone on from there and Roberts almost doubled the lead just before half-time when he bent a free-kick over the wall.
However debutant keeper Owain Fon Williams pulled off a brilliant tip-over save.
County, promoted via the play-offs in May, grew in confidence after the break with midfielder Stephen Gleeson, on loan from Wolves, going close.
Sub Carl Baker almost scored with a superb chip which fell just beyond the angle and then forced a diving save from Matt Glennon.
Roberts set up another chance for Booth but saw Williams block it on the line.
Stockport assistant manager Peter Ward was sent to the stand for protesting over decisions by referee Andy Haines in the second half, but his side held on for a point, to show that they can compete at a higher level.