There were few chances at either end throughout the 90 minutes with a draw a fair result on the balance of play.
After a quiet opening 15 minutes, Harris had the first opportunity, sending a low drive just inches wide of Joe Bursik's left-hand post.
Stoke midfielder John Obi Mikel came to his side's rescue, clearing off the line to keep out a firm drive from Harris.
Pulis made a change for the start of the second half, sending on Jordan Rhodes in place of Shaw.
Stoke made a strong start to the second period with Tyrese Campbell putting a shot on target which was saved by Wildsmith.
Vokes' header from the resulting corner was tipped over by the keeper.
Vokes also met a cross from Collins, but was unable to direct his header on target.
As Rhodes threatened to break through the centre, Danny Batth did well to get across and clear the danger.
A change for the visitors midway through the half saw Jordan Cousins take over from Mikel.
O'Neill made another substitution a few minutes later with McClean replaced by Jacob Brown.
Vokes went close to scoring a stoppage-time winner, firing on target from 12 yards out, but Wildsmith was equal to it, making a vital stop to ensure the game finished all-square.