Leeds, three-times English league champions, took the lead when Polish midfielder Mateusz Klich beat Jack Butland from close range before Pablo Hernandez added a second before halftime as his shot deceived the keeper at Elland Road.
Benik Afobe, one of four Stoke players making their debuts after joining on loan from Wolverhampton Wanderers, got a goal back for the visitors with a penalty after the break when Barry Douglas fouled Tom Ince, who had hit the bar in the first half.
But Scotland defender Douglas made up for his error when his corner was headed home by captain Liam Cooper to complete a fine display and give new Stoke boss Gary Rowett plenty to ponder.
Bielsa, who has managed clubs in Argentina, Spain and France plus Chile's national team, replaced Paul Heckingbottom, who was sacked after Leeds finished 13th in the second tier last term.
Rowett, 44, was appointed Stoke manager in May on a three-year contract after Stoke agreed a compensation package with Derby County, whom he had led into the playoffs last season.
Stoke sacked Mark Hughes in January and parted company with his replacement Paul Lambert after the Midlands club's 10-year stay in the top flight came to an end last term.
(Writing by Ken Ferris; Editing by Clare Fallon)
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