They have also smashed two further club records for straight wins and straight shutouts.
It was the home side who opened the brightest on a mess of a pitch at Edgeley Park. Just six minutes had gone when young midfielder Anthony Pilkington turned neatly on the edge of the box before firing a low drive narrowly wide.
Jason Taylor saw a shot comfortably saved by Town 'keeper Phil Smith, but at the other end minutes later, Wayne Hennessey was more acrobatic when tipping over a fine Lee Peacock header.
However, it was Stockport who opened the scoring on 15 minutes with a smart breakaway goal. Adam Proudlock whipped in a tempting cross from the right, and there was Anthony Elding who slid home his sixth goal for the Hatters from eight yards.
Just before the half-hour mark Swindon had a great chance to get back on terms, but Peacock shot straight at Hennessey after racing clear.
Taylor was putting in a great effort in the County engine room, and he was unlucky when he smashed a shot inches over from 25 yards.
Blair Sturrock had another decent chance to level things up on 43 minutes, but again Hennessey was equal to the task.
County deservedly went further in front on 50 minutes following a good piece of opportunism from Elding. He latched onto Ashley Williams' free-kick, turned sweetly and then smashed home from 15 yards.
Stockport defender Michael Rose saw a curling 20-yard free-kick saved by Smith, while at the other end Jamie Vincent planted a free header wide from just six yards.
Elding went agonisingly close to a third goal on 70 minutes, but he somehow screwed a shot wide from just six yards.
Town's Jerel Ifil was then sent off for a second yellow card to cap a miserable afternoon for the Wiltshire men.
A clinical 85th-minute finish from sub Liam Dickinson wrapped it up for buoyant Stockport.