The Mariners' supporters turned up in numbers to get their vouchers for the Carling Cup second round home tie against Tottenham and at half-time looked set to get the bonus of seeing a league victory.
Grimsby started slowly and then started to play some good stuff and it was only a matter of time before the goal came.
It duly arrived after 33 minutes when Andy Parkinson and Calvin Andrew combined to give Gary Jones a simple chance from close range.
The scoreline stayed that way until the 11 minutes after the break when Grimsby skipper Justin Whittle sliced a clearance high into his own net to bring the visitors level.
Jermaine Easter then dragged a great chance wide as Stockport gained the upper hand.
When Grimsby goalkeeper Steve Mildenhall had to come out of his area to clear on 75 minutes Easter chipped the ball towards goal and midfielder Matt Hamshaw headed neatly home.
Worse was to befall the Mariners four minutes later when Frenchman Mickael Wolski let fly from 25 yards and saw his shot fly into the bottom corner.
This left Grimsby and their fans stunned and, despite a couple of substitutions, there was no way back for the home side, who have won both their away games but have already lost twice at home.
It was County's first win of the season but that had looked unlikely in the first half when Grimsby were in control and looking odds on to record their second win of the week.