A goal in either half was enough for Oldham to extend their red-hot run of form and keep them in second place in the Division Two table.
The Latics have now won 9 out of 11 in the league and had defender Fitz Hall and teenage debutant Scott Vernon to thank for their latest success.
Stockport worked hard in a tense local derby, only to come a cropper against the home side's defensive brick wall.
County boss Carlton Palmer, however, took heart from his team's performance at a rain sodden Boundary Park.
Palmer said: "Oldham were promotion favourites at the start of the season and we knew they would be strong, we came here to win so I am disappointed but we acquitted ourselves well.
"There wasn't much between the teams even though we are a very young side and Oldham have a lot of experience.
"Our final ball wasn't good enough but there were plus points and the young lads we'll keep learning if they stick with me." Oldham almost lead after four minutes when Hall was denied by a goal line clearance from Aaron Lescott.
Stockport had their best spell midway through the half, going close through Karim Fradin and winger Kevin Ellison.
The home side went in front after 40 minutes when Clint Hill helped on a corner and Hall used his 6 ft 4 frame to nod in from close range.
Oldham then took over and had a series of chances which Wayne Andrews, Josh Low and Carlo Corazzin were unable to capitalise on.
County thought they had levelled seven minutes from time, but a long range piledriver by Ali Gibb went inches wide with the keeper beaten.
Vernon made sure of the points in stoppage time when he ran on to Chris Killen's flick and slid home from 10 yards.
Oldham manager Iain Dowie said: "This was a resounding performance although we can still do better. Our passing and movement were good and we stayed solid at the back."