County 'keeper James Spencer had little to do, while opposite number Phil Barnes was busy almost all afternoon.
Stockport have been in great form at home of late, but they were assisted by a soft own goal after just seven minutes. Left-back Michael Rose swung in a dangerous corner-kick from the right, but Barnes, who was under no pressure, got his bearings all wrong and punched the ball into his own net.
County skipper Tony Dinning then tried an audacious chip from all of 40 yards, but the ball sailed over Barnes and a couple of feet over the crossbar.
The rain was constant and the challenges were flying in, and as Stockport youngster Anthony Pilkington tried to skip past Nick Fenton in the box on 24 minutes, the Grimsby defender appeared to handle the ball as he slid in and a penalty was given. Referee Mr Miller red-carded Fenton, but Stockport striker Liam Dickinson promptly smashed the penalty kick against the post.
However, Dickinson quickly atoned for that error when he turned home a smart Pilkington cross to increase Stockport's lead on 29 minutes.
Down to 10 and now two behind, it was turning into a shocking day for Alan Buckley's side, and before the break both Pilkington and Dickinson came close to increasing the home side's lead further.
Pilkington volleyed straight at Barnes on 52 minutes, then seconds later Jason Taylor curled a sweet shot a whisker past the far post.
It was all Stockport, and just before the hour mark defender Rob Clare found space in the Grimsby box, but his low drive struck a post.
Adam Griffin was next to test Barnes with a rasping low drive, but substitute Michael Malcolm wrapped things up 13 minutes from time when he skipped past two Town defenders before curling home a sweet shot from 20 yards.