Notts lost the game despite taking a confidence-boosting lead as early as the seventh minute.
Lively newcomer Felix Bastians, on-loan from Nottingham Forest, won two early corners for his new club and the second, taken by Neil MacKenzie, was headed through by defender Stephen Hunt who from the first corner had headed over.
Notts, however, failed to hold their lead for long when Stockport's front
Dickinson knocked the ball into Elding's path and the leading scorer finished crisply leaving Kevin Pilkington with no hope of making a save.
The Notts defence, which had been reshaped to accommodate debutant Guy Branston, was struggling badly against the lively Hatters but the second goal - which turned out to be the winner - was a scrappy affair.
Notts failed to clear a right-wing corner and the ball was turned over the line by Dickinson from close range.
Stockport held their lead comfortably until the break when Notts manager Ian McParland replaced Branston and also the ailing Richard Butcher in midfield.
Notts were definitely better in the second half and had two great chances of an equaliser which, on the balance of play overall, they just about deserved.
First, Bastians rattled the left-hand upright of Stockport goalkeeper Conrad Logan and moments later, with a 25-yard free-kick, MacKenzie thudded the ball against the angle of post and bar.
Though the Magpies kept plugging away spiritedly, such clear chances never came their way again although Krystian Pearce with a header and Spencer Weir-Daley, who came off the bench to produce a shot, went reasonably close.
Stockport's travelling 650 fans were in ecstasy at the end knowing the Hatters had won three times in a row for the first time this season.
Notts, however, had no such cheer to contemplate as their wretched home form continues.