Marcelo Bielsa made one enforced change for the trip to Staffordshire as Liam Cooper dropped out of the squad through injury to be replaced by Gaetano Berardi.
It was the hosts who started the better of the two sides at the bet365 stadium as Nathan Jones made six changes to his line-up.
Liam Lindsay sliced a chance wide from a corner before Lee Gregory also saw a shot blocked in the early exchanges.
United, though, had the first real opening of the game as Adam Federici was forced into action after an Adam Forshaw shot fell to Pablo Hernandez who saw his effort punched clear.
The rebound fell to Mateusz Klich inside the box but the Pole was also denied as the City defence swarmed.
Stoke continued to push forward but it was Bielsa's men who opened the scoring with a wonderful move on the stroke of half-time.
Forshaw won the ball on the halfway line and shrugged off his marker with a pass to Harrison inside the hosts half.
The winger found Hernandez at the first attempt who in turned played a defence splitting pass to Dallas inside the box.
The Northern Irishman beat James McClean to the ball and pounced to slot home with a neat finish low past Federici.
It took just six minutes for the visitors to double the advantage following the half-time interval through another well-worked move.
Hernandez found Patrick Bamford inside the area with the forward drilling low to the back post where Alioski was waiting to smash home.
Leeds again added to the scoreline as Bamford this time got himself on the scoresheet.
Alioski this time latched onto another perfectly placed ball from Hernandez, before the Macedonian saw his shot rebound into the path of Bamford who made no mistake as he drilled home from close-range.
Substitute Helder Costa almost added a fourth late but Federici thrust himself to his right to tip the curling effort wide of the mark.
Leeds, though, had to settle for three as they headed back to West Yorkshire with a fourth win from five league fixtures which sees them sit top of the pile.