On-loan Stoke striker Paul Gallagher had the only shot on target in the first half after Shaun Derry lost possession but Neil Sullivan held on.
Rob Hulse's header and David Healy's shot forced Steve Simonsen into saves as the game improved after the break.
Hannes Sigurdsson went close and Darel Russell's 25-yard drive was tipped wide before Rob Hulse's header hit the post.
Stoke boss Johan Boskamp:
"We are happy with the result. Stoke have played better games than this. A point was good for us, but the way we played wasn't so impressive.
"We let them come at us and get crosses into the box, but luckily for us every loose ball fell to us and not for them.
"I saw Leeds play against Coventry and it looks like they are having difficulties scoring goals."
Leeds: Sullivan, Kelly, Butler, Gregan, Crainey, Miller, Douglas (Blake 68), Derry, Lewis (Griffiths 74), Hulse, Healy (Beckford 63).
Subs Not Used: Bennett, Kilgallon.
Booked: Gregan, Butler.
Stoke: Simonsen, Hoefkens, Duberry, Hill, Buxton, Mbuyi (Brammer 61), Russell, Paterson, Gallagher (Sweeney 74), Sidibe, Bangoura (Sigurdsson 45).
Subs Not Used: de Goey, Broomes.
Ref: K Stroud (Hampshire).