The Potters remain stuck on one Premier League win in 2013 but recorded their first clean sheet since November which will be a welcome return to their mid-season form.
A point for West Brom keeps their faint hopes of securing European qualification alive, while Stoke have edged slightly ahead of the relegation pack but their first top-10 Premier League finish could still elude them this season.
Stoke were handed a pre-match boost as Matthew Etherington overcame a fitness scare to start, with Andy Wilkinson dropping to the bench. Clarke opted for Romelu Lukaku up front for the Baggies, leaving Shane Long and Peter Odemwingie on the bench.
West Brom started the livelier side as they applied the pressure on the Potters in the opening minutes of the tie, with Chris Brunt forcing Asmir Begovic into an early save after James Morrison put in a through ball for the midfielder.
Despite a rocky start, Jonathan Walters went on to have the best chance of the first half as his shot deflected off Olsson before creeping inches wide of Ben Foster's goal.
A lack of chances on goal led to Pulis bringing on Dean Whitehead for Glenn Whelan at half-time, but it was West Brom who started the second half brightly. Thomas’ cross was met by Lukaku's header but the effort was comfortably dealt with by Begovic.
Clarke’s side continued their dominance as West Brom repeatedly attacked via the right flank as Morrison’s crosses provided a challenge for Stoke to deal with, although Lukaku failed to make use of his opportunities.
Kenwyne Jones was introduced just after the hour mark at the expense of Peter Crouch, before West Brom responded by bringing on Odemwingie for Thomas, and the Nigerian immediately made an impact as his 25-yard strike was saved by Begovic.
Stoke came agonisingly close to the opening goal with 10 minutes to go, as Marc Wilson’s header travelled inches wide of the goal following Whitehead’s corner.Despite late chances from Charlie Adam and Kenwyne Jones, West Brom held firm to gain a point.