Inspired Stoke goalkeeper Asmir Begovic denied Albion victory in an entertaining game at the Britannia Stadium.
The Baggies had the better of an end-to-end clash but three fine saves from Begovic was enough to earn the Potters a point.
He denied Stephane Sessegnon with an excellent flying save then thwarted Morgan Amalfitano with a brave block before half-time.
And in the dying seconds he did superbly to keep out another shot by Sessegnon after referee Howard Webb had denied the visitors a clear penalty when Charlie Adam fouled Youssouf Mulumbu.
But the point means the Baggies are now unbeaten in five Premier League games following their slow start to the season.
After an open start to the game, it was Albion who had the first clear chance on 19 minutes.
A neat move ended with a through-ball from Saido Berahino finding Sessegnon, who saw his right-footed shot saved superbly by Asmir Begovic in the Stoke goal.
Stoke broke to the other end immediately and created a chance of their own with some patient play.
The ball eventually fell to Jonathan Walters but his shot from the edge of the penalty area presented Boaz Myhill with a comfortable save.
But it was the Baggies who held the upper hand and went close again when Victor Anichebe peeled out wide and delivered a dangerous cross to Sessegnon.
The Benin international connected with a first-time shot but it curled just wide.
And Begovic came to Stoke’s rescue for a second time midway through the opening half after a neat link-up between Berahino and Sessegnon teed up Amalfitano, darting in from the right.
The Frenchman took a touch and attempted to chip the ball over the advancing Begovic, who made a good, low save.
But, having been pegged back, the home side enjoyed a decent spell as half-time approached and Claudio Yacob had to make a vital interception to cut out a cross-shot from Stephen Ireland following a clever free-kick from Marko Arnautovic.
Albion started the second half well and compiled an excellent passing move that ended when Liam Ridgewell’s dangerous cross from the left was cut out at the near post.
And they should have had a penalty just before the hour-mark when Billy Jones found Mulumbu in the box and his heel was clipped by Adam, but referee Webb waved away the protests.
Stoke had been second best but they missed a glorious chance midway through the second half when a pacy run from Arnautovic on the right caught the visitors on the break.
His cross gave Ireland the best chance of the game but the former Villa man’s shot narrowly cleared the crossbar.
And Adam almost caught out Myhill with 17 minutes remaining when he hit an audacious lob from the halfway line, but the Baggies keeper scrambled back and pushed it over the crossbar.
Albion continues to press in the closing stages but a 25-yard effort from Mulumbu curled just wide of the target.
In the final minute Sessegnon cut in from the left and jinked past two defenders but saw his shot saved superbly by Begovic.
West Brom boss Steve Clarke said: "It's a good point but it's disappointing we didn't get all 3.
"We had the better chances.
"We were denied a stonewall penalty for Adams' foul on Youssouf. It's a penalty from every angle you look at it.
"We controlled most of game and their keeper winning man of match underlines balance of play. Overriding feeling is of disappointment."