Michael Raynes' clearance only went as far as Robert Snodgrass allowing the Leeds' winger to run at the County defence before shifting the ball onto his left foot and beating Owain Fon Williams from 18 yards.
The 3,000 plus Leeds fans inside Edgeley Park might have expected the floodgates to open but after 12 minutes the home side were level.
Carl Baker, back after a three-game ban, was pulled back by Patrick Kisnorbo on the edge of the box and the Hatters' top scorer picked himself up to slot a low free kick past Casper Ankergren and into the bottom corner.
And as the frantic opening continued, Fon Williams pulled off an acrobatic one-handed save to deny Luciano Becchio, David Poole forced Ankergren into a double save from close range and Bradley Johnson hit the bar with a dipping volley from 20 yards.
Then, on the hour mark, the Hatters stunned Leeds by taking the lead when Poole's cross was bundled in by Johnny Mullins for his first goal of the season.
Simon Grayson immediately threw on Jonathan Howson and Max Gradel in search of an equaliser and within seven minutes they were level.
Kisnorbo crossed deep into the County area and Fon Williams was beaten to the ball by Jermaine Beckford who headed into the empty net.
It was a cruel blow for the Hatters and three minutes from time they were dealt another one when Richard Naylor laid the ball across the edge of the box for Leigh Bromby to thump home.
And as County pushed forward Leeds broke quickly and Beckford raced clear to slide the ball past the onrushing Fon Williams before Poole was sent off for a lunging challenge on Max Gradel in stoppage time.
Stockport County 2 (Baker 12, Mullins 62)
Leeds United 4 (Snodgrass 2, Beckford 67, 90, Bromby 87)
Stockport: Fon Williams, Mullins, Turnbull, Raynes, Vincent, Thompson (Johnson 76), Baker, Griffin, Poole, Ribeiro, McNeill.
Leeds: Ankergren, Bromby, Naylor, Kisnorbo, Hughes, Snodgrass (Gradel 65), Kilkenny, Doyle, (Howson (65), Johnson, Becchio (Kandol 76), Beckford.
Referee: Kevin Friend