QPR's Kevin Gallen slotted home a winning penalty a minute from time for his ninth goal of the season.
It was the Rangers top scorer who was up-ended inches inside the box by Anthony Tonkin after Richard Pacquette's pass had put Gallen in the clear.
The Rangers player picked himself up and fired low and beyond the right hand of keeper Lee Jones.
Up until then a 0-0 draw was the best bet even though Pacquette had headed against the base of the post on 70 minutes.
A solid Stockport defence marshalled by player-boss Carlton Palmer deserved at least a share of the points.
County had the first chance of the game when Daniel Shittu's slip gave quick thinking Luke Beckett a chance to lob the keeper from 20 yards, but the attempt drifted just over the bar.
In the space of a minute either side could have taken the lead.
Steve Palmer sprinted away on the left but his intended centre for Marc Bircham took an age to arrive and the Rangers midfielder completely missed his kick.
County broke away to the other end and Ben Burgess went for power with only the keeper to beat but only ended up blasting his angled shot high and wide from seven yards.
On the stroke of half time Palmer felled Lee Cook on the edge of the box and the Stockport manager fought himself into the book for arguing.
Palmer breathed a sigh of relief when Richard Langley's free-kick sailed over the bar.
Another dead ball delivery from the midfielder on 50 minutes was won by Brett Angell on the back post, whose header fell to Cook, but his stab at the target was saved on the line by John Hardiker.
At the other end Palmer nearly made amends when his header missed Beckett by a whisker with the goal at the mercy of the County striker.
Gallen then found his range with a rising right foot shot from 15 yards to bring a great save from Jones.
However he gave the keeper no chance with what ended up becoming almost the last attempt of the match to seal the win.