Harpal Singh and Kevan Hurst combined to put County ahead at Boundary Park before Hurst created the killer second goal for top-scorer Warren Feeney.
Stockport boss Chris Turner has already admitted his side are doomed to the drop but he made seven changes from last week's defeat to Port Vale and saw a battling response.
Oldham are sliding deeper into trouble themselves and their defeat followed a 4-0 hammering at Bournemouth and a 5-3 home loss against Wrexham.
Oldham should have gone in front early on but winger Kevin Betsy fired straight at keeper James Spencer after being set up by a surging run from Mark Hughes.
There were also chances for Neil Kilkenny, Hughes and Will Haining, whose header from a corner was cleared off the line.
Stockport bounced back to score after 37 minutes as Singh crossed from the left and Hurst nipped in at the near post to flick the ball into space and slot in from six yards.
Betsy hit another chance at Spencer for Oldham who went 2-0 down on the hour mark.
Stockport's second was a quick and incisive counter attack which saw Hurst deliver from the right and Feeney dive spectacularly eight yards out to bury a header.
Oldham replied on 70 minutes when Scott Vernon touched in from six yards after being found by veteran David Eyres.
It was Stockport who came closest to adding another in the closing stages through Feeney and they held on with few problems.