Dennis Wise's side now have the honour of Swindon's best start to a league campaign in 43 years after five straight wins.
Stockport were no match for a Swindon team should have added more to the two goals they scored through Aaron Brown and Christian Roberts.
Wise was given an early scare when a young midfielder Andy Caton was forced off for stitches on a head injury following a nasty clash with County full-back Michael Bowler.
Despite all their first half possession Swindon huffed and puffed in front of goal without really finding the necessary penetration take the lead.
And it was Stockport who almost broke the deadlock when defensive cohorts Ashley Williams and Gareth Owen combined, only for Owen's header to drift just wide.
Swindon quickly sparked into life and took the lead three minutes later through Browns cleverly work free-kick.
As County goalkeeper James Spencer was expecting an effort from set-piece specialists Paul Evans and Roberts, Brown set up to smash a left-footed strike into the corner of the net.
Spencer redeemed himself just minutes later when Lee Peacock crossed from Roberts to head unmarked only to the goalkeeper to somehow to claw away what seems a certain goal.
Just before half-time Ricky Shakes was unfortunate to see his long-range dipping effort come back off the crossbar.
Stockport boss Jim Gannon introduced Tes Bramble in the hope of finding an equaliser, but it was the home side who continued to press for the second crucial goal.
Peacock stunned Spencer into action in the hour mark before Roberts was unlucky to see his goalbound half-volley deflected wide by County defender Williams.
The Welsh striker didn't have long to wait before finally getting on the scoresheet minutes later.
Roberts turn sharply on the corner of the penalty area before sending his right-foot finish past the outstretched arm of Spencer for his second goal in many league games.
As Stockport looked for a consolation, Shakes was then guilty of the miss of the afternoon when he somehow headed wide unchallenged from six yards following Brown's run and cross.