After Asmir Begovic kept out an early strike from Albion captain Chris Brunt, the hosts - who went into the contest having lost their last three Barclays Premier League games and seven of their previous nine - were the better side in a scrappy first half.
They could not pose any great threat to the Baggies goal, though, with a deflected Jon Walters effort being their closest attempt.
The match improved slightly after the break, but neither team could find a winner, with West Brom's Romelu Lukaku and Stoke's Peter Crouch unable to convert headers.
Potters substitute Kenwyne Jones passed up a good opportunity in stoppage time, with Ben Foster claiming his shot.
The result sees Stoke move up to 10th place in the table, while Albion stay eighth.
West Brom won a free-kick in a promising position in the second minute after Ryan Shotton slid in on Jerome Thomas, but Lukaku could not fashion a decent shot when the set-piece was laid to him.
A minute later Brunt sent a speculative attempt into the stand, before Cameron Jerome looped a header over the bar at the other end.
Brunt then broke into the box and hit an effort at Begovic, who gathered at the second attempt.
It had been a fairly lively opening from the Baggies, but the hosts began to settle down from there, albeit without carving out any really clear-cut opportunities.
Geoff Cameron chested down from a failed attempted clearance by West Brom and fired off-target, and there were then claims that Foster had handled the ball outside the area.
Referee Mike Dean judged that the England goalkeeper had been fouled by Jerome on his way out of the box and awarded a free-kick to the visitors.
Crouch was next to send a header too high, before Walters saw a shot from outside the box deflect off Jonas Olsson and spin just wide.
Jerome whipped the ball across the area on the turn just after the half-hour mark, but it went out for a throw-in.
The general lack of tempo in a poor first-half was summed in the 34th minute when Dean booked Brunt for time-wasting.
Stoke midfielder Glenn Whelan, who had been on the receiving end of a high boot from James Morrison at the end of the first half, was substituted for Dean Whitehead at the interval.
Shortly after the restart, the in-form Lukaku - scorer of eight goals in his previous 11 Premier League games - got his head to a Thomas cross, but it bounced through to Begovic.
Within a minute, Crouch nodded the ball onto the roof of Foster's net from a Matthew Etherington delivery.
Marc Wilson, again playing at centre-back for Stoke in the absence of the suspended Robert Huth, then headed the ball away when Lukaku just failed to make connection with Liam Ridgewell's cross into the danger zone.
West Brom continued to press, with Begovic getting a palm to a ball into the six-yard box and it going over via another player - seemingly Lukaku, although Dean gave a corner.
Stoke manager Tony Pulis reacted by bringing on Jones for Crouch, while Albion boss Steve Clarke replaced Thomas with Peter Odemwingie.
More substitutions followed, with Charlie Adam coming on for Jerome and Lukaku being withdrawn for Shane Long, but it made little difference to proceedings.
Youssouf Mulumbu struck off-target with around 15 minutes remaining and Wilson then headed wide from a corner.
Ryan Shawcross fired a shot against Foster towards the end, but the assistant linesman's flag was raised.
Jones was in a similar position in the box at the death and onside as he chested the ball down, but he could not put his shot beyond Foster.