Rory Fallon scored his first goal for Swindon of the season so far after 13 minutes from 8 yards out after a pass by new loan signing Jamie McMaster.
Mid way through the first half Rhys Evans had to make a good save to keep Swindon in the lead where he managed to deny Luke Buckett a goal with a one-on-one with Evans.
After Stockport came close again Swindon scored with new boy Jamie McMaster scoring seconds before half time. He scored from a goal mouth scramble, and just managed to force the ball across the line from close range to give Swindon a 2-0 away lead going into half time.
In the second half Stockport came out looking a lot stronger, and as usual Swindon just sat back.
Stockport came close to scoring with a free kick from the edge of the box which hit the post, then bounced up and hit the bar, but luckly for Swindon didn't cross the line before he was cleared away.
Brian Howard had a free kick from about the same distance he scored from against Bradford, but this time his shot was off target.
Then on 66 minutes Rory Fallon looked to have won the game for Swindon as he scored from close range to make it 3-0 to Swindon after being set bup by Jamie McMaster. A large number of Stockport fans left at this stage, and must now be wishing they hadn't.
Stockport pulled a goal back on 73 minutes when Luke Buckett lobbed the advancing Rhys Evans to score from 20 yards out to make it 3-1 to Swindon.
16 year old Andy Caton came on for Swindon to repace Jamie McMaster with 20 minutes to go.
After 75 minutes Stockport did the same as they did last season after it was also 3-0 to Swindon and pulled another goal back to make it 3-2 after a close range goal by Luke Beckett as Swindon failed to clear the ball away.
Then another mistake by the Swindon defence on 83 minutes lead to Stockport making it 3-3 Stuart Barlow scored from a cross from Cartwright.
Both teams pressed forward to both try and get a 4th goal, but the final score stayed at 3-3.
Overall a draw was a fair result, but Swindon should never have given away a 3-0 away lead. After giving away a 2-0 lead against Walsall in August Swindon should have known to not just sit back.