Tony Pulis' side went into the game with only one win in ten matches and although they controlled the first half, they couldn't force a breakthrough.
West Brom assumed the ascendancy after the break, but despite a trio of chances falling to Romelu Lukaku, they too were unable to grab a winner.
Both teams failed to impress in a poor first half desperately short on quality. Stoke showed no end of energy and commitment, but they were totally bereft of penetration going forward and created chances only from high balls into the box.
The first came after four minutes, when Cameron Jerome scooped a header over and wide from the penalty spot after a cross from Matthew Etherington on the left wing.
West Brom then had the best chance of the half a minute later through Chris Brunt, but having been played through on goal following a slick passing move, the Northern Irishman fired his low, left-footed shot straight at Asmir Begovic.
The visitors persistently struggled to retain possession and spent much of the opening period on the back foot, albeit defending the barrage of crosses into the box stoutly.
They improved considerably after the break, though, and should have gone ahead within two minutes of the restart, when Jerome Thomas planted a cross straight on the head of Lukaku, only for the Belgian to head down and into the arms of Begovic.
The on-loan Chelsea forward then spurned an even better chance seven minutes later. This time it was the marauding Liam Ridgewell who found him with a pinpoint left-wing cross, but Lukaku failed to make contact with the ball and Marc Wilson gratefully cleared.
He still wasn't finished, though, because just after the hour mark Begovic deflected a James Morrison cross on to Lukaku's face and the ball rebounded just the wrong side of the post.
West Brom manager sent on Peter Odemwingie and the controversial forward twice drew saves from Begovic with shots from outside the box, before Wilson went close at the other end for Stoke with a header from a corner.
The hosts thought they had won it at the death when substitute Kenwyne Jones brilliantly collected a high ball on his chest and stabbed a shot goalwards, but man-of-the-match Ben Foster was right behind it.