Connor Jennings made his debut for the Hatters alongside his former Stalybridge team mate Craig Hobson as County lost back to back league games for the first time since August.
The result could have been so different had the new striker's header from a Matt Mainwaring cross, in the first minute found the net instead of being tipped over by keeper Adam Smith.
The Hatters had earned three corners before the home side even ventured into their half, Ian Ormson saving comfortably from Andy Brown on 7 minutes.
In a half of almost constant pressure from County, Hobson and Jennings both had efforts saved by Smith, Tom Collins also testing the keeper with a free kick.
Collins however saw his afternoon ended early as he was replaced by Danny Whitehead on 27 minutes.
The home side finally created a chance when Brown beat James Tunnicliffe in the air only to see Tom James deliver a poor cross to waste the chance.
Whitehead and Alex Kenyon had crosses cleared before a brilliant move between Whitehead and Hobson saw Smith tip the ball away for another corner, Sean Newton firing over from 25 yards after the ball had been cleared.
Ormson was tested for the first time, making the save off the half in the last minute diving to his right to keep out shot from outside box. Incredibly after over 40 minutes of one way traffic the Hatters went into the break a goal down.
After a poor challenge on Jennings went unpunished, Town broke down the left in the second minute of added time, Brown heading home to give his side the lead with only their second effort on goal.
HT: Nuneaton Town 1 Stockport County 0
County started the second half on the front foot as good play from Tunnicliffe and Mainwaring brought an early chance for Hobson, home skipper Gareth Dean defending well to deny the Hatters front man.
Buoyed by their opener the home side looked a different proposition with Simon Forswick driving an effort over the bar after good work by Brown. Ormson then making a great save to deny Tyrell Waite after an error from Joe Connor.
On the counter attack Paul Turnbull played in Whitehead, Smith was quickly off his line to make the save. Whitehead appearing to have taken a knock in the buildup play.
Top scorer Danny Hattersley replaced Whitehead on 57 minutes with Sam Sheridan also replacing Turnbull.
Sheridan was immediately in action with a superb through ball which found Hattersley in the box. The striker clipping the ball over the advancing Smith before appearing to be taken down. Referee Whiteley waving away appeals for a penalty.
Newton and Jennings went into the referee's note book for the type of fouls that had gone unpunished when committed by home players before the home side were awarded a penalty for a coming together in the box on 80 minutes. Adam Walker slamming home the resulting spot kick.
County's players had further reason to feel aggrieved as they were denied a clear spot kick of their own a few minutes later as a blatant handball in the box went unpunished before Hobson appeared to be dragged down on the edge of the box, again nothing given. To add insult to injury for the County striker it was he who was punished after keeper Smith dropped a Sheridan cross in the last minute of the game.
FT: Nuneaton Town 2 Stockport County 0
Starting XI: Ormson, Newton, Connor, Tunnicliffe, Kenyon, Collins (Whitehead), Hobson, Fagbola, Mainwaring, Turnbull (Sheridan), Jennings.
Subs: King, O'Donnell, Whitehead (Hattersley), Hattersley, Sheridan.
ATT: 1,221 (687)