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Tony Pulis’s side had taken the lead early in the second half through a Matthew Etherington penalty and substitute Walters came off the bench to net from the spot himself before grabbing his second in stoppage time.
That takes Pulis’ team up to eighth in the Premier League as they built on victories over Birmingham and Liverpool, while the Baggies have now lost four of their last five league fixtures.
West Brom striker Peter Odemwingie drilled a low shot straight at Asmir Begovic early on before Youssouf Mulumbu rifled an effort from outside the area which rose too high.
Odemwingie threatened again as he twisted and turned before hitting a tame effort which Begovic gathered comfortably.
But Stoke regrouped at half-time and took over in stunning fashion after their 55th-minute opener.
Ricardo Fuller laid off to Kenwyne Jones, who initially appeared to have let the ball slip past him but got a touch just as Albion goalkeeper Scott Carson was diving at his feet.
Although contact looked to be minimal, Jones went down in the area and referee Chris Foy awarded the penalty which Etherington calmly dispatched into the bottom corner.
Baggies boss Roberto Di Matteo sent on Somen Tchoyi and the Cameroon midfielder saw his header from a Jerome Thomas cross tipped over by Begovic as the hosts piled on the pressure.
Odemwingie thought he had been fouled having fallen in the box under a Robert Huth challenge, but it was Stoke who won another penalty in the 85th minute.
Dean Whitehead was clattered by Simon Cox as he ran on to a Tuncay Sanli 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.
With an impressive portfolio of projects, Al Bateen offers a vast range of high-quality fasteners across industries
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