The first chance arrived on seven minutes when a well worked move saw Mamady Sidibe's lay-off for Dave Brammer produce a 25-yard low drive that Neil Sullivan was forced to save low to his right.
The game took a twist when after Paul Gallagher's shot was spilled, the arriving Sidibe was chopped down in the area by both the sprawling goalkeeper and Gary Kelly to concede an 18th minute penalty.
However, the usually clinical Gallagher had his spot-kick brilliantly saved by Sullivan in his bottom left corner a minute later.
Leeds almost shot themselves in the foot again in the 27th minute when John Halls' cross from the right was inches away from being turned into the net by opposing captain Paul Butler.
The visitors nearly claimed a largely undeserved goal four minutes before the break when Jonathon Douglas collected the ball on the edge of the box but his shot drifted wide of Steve Simonsen's post.
Even after a change of referee things continued much the same way with Stoke having the lion's share of attacking play.
Both Luke Chadwick and Darel Russell went close but the scores remained level.
However, City were dealt a cruel blow in the 69th minute when Douglas' sweeping low cross from the right was missed by Richard Cresswell but presented Eddie Lewis with a simple finish from six yards.
Sullivan did well again to keep his side's slender lead in tact, first saving a vicious Sam Bangoura shot and then palming substitute Hannes Sigurdsson's long-range drive around his post.
The away supporters were made to sit on the edge of their seats right until the death as former Leeds player Michael Duberry somehow hit the crossbar with a seemingly easy four-yard shot in stoppage time.