Matthew Etherington’s penalty put the visitors 1-0 up in the 55th minute on Saturday after referee Chris Foy adjudged Scott Carson to have fouled Kenwyne Jones.
Substitute Jon Walters converted another spot-kick with five minutes of normal time remaining and then bagged his second at the death to make it three wins out of three for the Potters.
That takes Tony Pulis’ side, only recently hovering around the relegation places, up to eighth in the table as they built on victories over Birmingham and Liverpool.
The result brings more disappointment for the Baggies, though, who have now lost four of their last five league fixtures.
The hosts looked to make an early impression with Peter Odemwingie having a shot deflected wide in the first minute.
The Nigeria striker then whipped a free-kick straight into the arms of Asmir Begovic, but Stoke were soon launching an attack of their own, with Jermaine Pennant just unable to control his attempted cross having collected the ball in the box from Etherington.
It seemed Pennant had picked up an injury and within seconds he was withdrawn, Pulis throwing Tuncay Sanli into the fray.
Odemwingie almost found himself in the clear as he tried to bring down Carson’s long kick but Foy halted the action to speak to Ricardo Fuller and Gabriel Tamas, who had been involved in a flare-up.
Odemwingie then drilled a low shot straight at Begovic before Youssouf Mulumbu rifled an effort from outside the area which rose too high too soon.
Albion upped the tempo slightly with Giles Barnes sending in a series of crosses from the right flank around the half-hour mark.
One fell to Jerome Thomas, who struck the ball against a Stoke shirt, while another was just inches away from being met by James Morrison’s head.
Fuller was crowded out in the box at the other end before he could fashion a strike and Odemwingie blasted a free-kick over the bar after Tuncay had brought down Thomas.
Odemwingie then twisted and turned but could only hit a tame effort which Begovic gathered comfortably.
The Baggies began the second period brightly, with Thomas sending in a cross that bounced off Odemwingie’s knees and Morrison just beaten to a delivery by Barnes.
But 10 minutes after the restart, it was the Potters who opened the scoring.
Fuller picked up the ball after Albion failed to clear a cross and laid it to Jones, who initially appeared to have let it slip past him but got a touch just as Carson was diving at his feet.
Although contact looked to be minimal, the Trinidad and Tobago frontman went down in the box and Foy awarded the penalty which Etherington then calmly dispatched into the bottom corner.
Baggies boss Roberto Di Matteo responded by introducing Simon Cox for Morrison and after Dean Whitehead sent an effort high over the bar, Somen Tchoyi was the next man to come off the home bench in place of Barnes.
Tchoyi was straight into the thick of things and angled a low delivery into the danger zone which Stoke managed to kick away.
The Cameroonian then saw his header from Thomas’ cross tipped over by Begovic as the hosts piled on the pressure.
Marek Cech blazed over soon after and Cox’s low shot from distance deflected wide before Di Matteo made his final substitution, with Graham Dorrans replacing Mulumbu.
Odemwingie thought he had been fouled having fallen in the box under the attentions of Robert Huth, but it was Stoke who won another penalty in the 85th minute.
Whitehead was clattered by Cox as he ran on to a Tuncay pass and Walters – on moments earlier for Etherington – converted the spot-kick.
Walters was not finished there either, receiving the ball from Jones’ flick in stoppage time and having one shot blocked before beating Carson to wrap up a comprehensive win.