Dennis Wise's side responded well to going behind to Mamady Sidibe's header from Lee Hendrie's right-wing cross and were level before the break.
Ian Moore's stooping header gave the visitors hope but Stoke struck when Ugo Ehiogu diverted a Patrik Berger shot beyond goalkeeper Tony Warner.
Stoke killed off the game when Ricardo Fuller profited from poor defending.
Leeds assistant boss Gus Poyet:
"It is difficult to analyse because the first half was the best we have played in the last month.
"Most people probably expected us to fold after going behind early, but we proved them wrong and played very well.
"But the pace of our play slowed and we got punished for making mistakes. Things are not going for us and we must work hard to make sure the tide turns."
Stoke: Simonsen, Hoefkens, Duberry, Higginbotham, Hill, Lawrence, Russell, Diao, Hendrie (Berger 46), Sidibe, Fuller (Pericard 81).
Subs Not Used: Brammer, Sweeney, Dickinson.
Goals: Sidibe 12, Ehiogu 54 og, Fuller 77.
Leeds: Warner, Richardson, Ehiogu, Heath, Lewis, Westlake (Kandol 61), Douglas, Derry, Howson, Healy, Moore. Subs Not Used: Sullivan, Carole, Rui Marques, Beckford.
Goals: Moore 41.
Ref: A D'Urso (Essex).