Luke Beckett scored his fourth goal of the season to earn Stockport victory at the County Ground but their real hero was Welsh goalkeeper Lee Jones.
Beckett struck the only goal of the match in the 56th minute in a rare Stockport breakaway.
Ben Burgess had a shot blocked near the line from a centre by Keith Briggs but the rebound fell into the path of Beckett who made no mistake from close range.
But it was at the other end where most of the action was centred and where the tall Jones made a series of outstanding saves.
Jones began by keeping out a low shot in the 12th minute from the busy Jimmy Davis and continued by denying Andy Gurney, Eric Sabin and Stefani Migiloranzi.
But Jones reserved his best for the 53rd minute with an outstanding double block to prevent Sam Parkin and then Gurney snapping up the rebound from six yards.
Jones went on to prevent Davis equalising and then in the 67th minute when he was beaten at last, a header from Parkin was cleared off the line by Jim Goodwin.
In contrast Swindon goalkeeper Bart Griemink had little to do.
But in the first minute he was forced into a good save to prevent Burgess opening the scoring and in the 23rd minute got down to his right to turn away a goalbound header from Beckett.
Referee Joe Ross booked four players, all from Stockport - Rob Clare and Dave Challenor for fouls and Ali Gibb and Carlton Palmer for time wasting as Swindon's pressure grew even more intense.
Swindon forced 12 corners, eight of them in the second half in a desparate bid to level but their setback was their defeat in succession whilst Stockport's victory was their third of the season