Mike Grella put Leeds on the way to a with a curler into the far post before Lubomir Michalik bundled in the second after 37 minutes.
Leeds had taken the lead through Grella in the ninth minute. Grella held off Johnny Mullins in the penalty area and laid the ball back to Bradley Johnson.
And when Johnson's heavy touch found its way back into the path of Grella, the American curled his shot past Fon Williams and into the far corner of the net.
Nicholas Bignall, deployed as a lone-striker, was a threat to the Leeds but County were restricted to long range efforts from Michael Rose and Carl Baker in the first- half.
Leeds could, and maybe should, have been reduced to ten men when Michael Doyle left David Poole in a heap after a high, reckless challenge.
Leeds boss Simon Grayson replaced Doyle before half-time to avoid the central midfielder being sent off after the referee chose not to, producing only a yellow card.
It was a decision that incensed the County bench, and eight minutes before half-time, referee Danny McDermid made another controversial decision.
Fon Williams looked to have been fouled by debutant Leigh Bromby as he came to claim Robert Snodgrass' free-kick but in the absence of the referee's whistle, Michalik stabbed the ball into the empty net.
With County boss Gary Ablett sent off, it was left to goalkeeper coach Paul Gerrard to man the technical area. But the referee was again at the centre of the action after 67 minutes when he pointed to the spot after Gianluca Havern handled Snodgrass' cross.
Snodgrass took the penalty himself but was denied by Fon Williams' legs.
Bignall twice tested Shane Higgs in the Leeds goal but even when County reverted to 4-4-2, they still couldn't find a way back into the game.
YEP Leeds United writer Phil Hay gives his Leeds United player ratings following the 2-0 win against Stockport County at Elland Road.
Shane Higgs: Higgs was actually selected on Saturday, a fact which could have been forgotten until he became involved in the second half. League One's clubs are struggling to get at him this season
Jason Crowe: Careless with possession on more than one occasion but was rarely stretched on the right and switched to centre-back competently enough when Bromby left the field
Leigh Bromby: Showed the qualities of a defender who knows when to play and when to do the sensible thing. Stockport looked more threatening after cramp curtailed his debut
Lubomir Michalik: After a long, inactive spell which must have punctured his confidence, Michalik can take heart from his rigid appearance, capped by a rare goal
Andrew Hughes: His versatility was shown by the fact that he played on both sides of defence, though he looked more comfortable at left-back than he did during 25 minutes on the right
Robert Snodgrass: Off the pace on Saturday and has still not found the level he reached last season. Placed his penalty too close to Fon Williams, with a predictable result
Jonathan Howson: Getting better by the game and was a class apart from every other midfielder on show. A more consistent final ball is all that could be asked of him at this stage
Michael Doyle: Booked for a fierce tackle on David Poole after 29 minutes and, in view of McDermid's erratic refereeing, removing him from harm's way before half-time was a logical ploy
Bradley Johnson: Swapped some important passes with Grella in the lead up to the opening goal but was fairly quiet. Helped to repel Stockport after switching to left-back in the second half
Luciano Becchio: Might have attempted to take centre stage with Beckford missing but stuck to what he does best by bullying and hassling the energy out of Stockport's defence
Mike Grella: Saturday's game was a big occasion for a player who has been a perennial substitute for United, and his cute strike was a dream moment. There is life without Beckford, it seems
Substitutes: Neil Kilkenny: (for Doyle, 41) Andy Robinson: (for Bromby, 64) Enoch Showunmi: (for Grella, 72)
Subs Unused: Tresor Kandol, David Prutton, Paul Huntington, Neil Kilkenny, Casper Ankergren.
Stockport: Fon Williams, Vincent, Mullins, Havern, Rose, Bridcutt, Pilkington (Johnson 59), Tansey, Baker, Poole (Griffin 78), Bignall (Thompson 84).
Subs Unused: Rigby, Turnbull, Halls, Rowe.