The hosts came into the game under little pressure, knowing Norwich City - who began Sunday in 18th position - needed to make up a three-point gap while also overturning a significant goal difference deficit.
Norwich were beaten by Arsenal, meaning that West Brom were assured of survival despite a fifth straight home loss at the hands of Stoke.
Stephane Sessegnon hit the bar from point-blank range for Pepe Mel's men early on, but the visitors soon seized control and moved ahead after 22 minutes courtesy of a Gareth McAuley own goal.
West Brom rallied after the break and levelled through a calm finish from Sessegnon, while Youssouf Mulumbu was denied by a post just after the hour.
Yet it was Stoke who sealed victory two minutes from time thanks to substitute Charlie Adam's strike from distance.
The result caps off a good campaign for Mark Hughes' side, who have secured a first top-10 finish in the Premier League and surpassed the 47-point haul they recorded in 2010.
Despite knowing that only a mathematical improbability would see West Brom relegated, head coach Mel insisted that this game represented his side's "biggest test" of the season.
And the hosts looked to have a spring in their step in the opening exchanges, nearly taking the lead inside three minutes when a frantic goalmouth scramble saw the ball fall to Sessegnon, who cannoned an effort off the underside of the crossbar from two yards out.
However, Stoke, who arrived with a 100 per cent Premier League record at The Hawthorns, responded well and almost took the lead six minutes later when Jonathan Walters raced away from the defence, before stinging the palms of Ben Foster with a well-struck drive.
The Republic of Ireland forward was at the centre of proceedings again within two minutes, somehow contriving to head wide from six yards after some great work down the right from Geoff Cameron.
But the visitors were rewarded for their efforts when a neat one-two inside the area allowed Marko Arnautovic to break free of his man before fizzing a low ball across goal that was turned in by a despairing McAuley.
West Brom struggled to find any sort of rhythm in the opening half, but were level 11 minutes after the break.
A sweeping counter-attack ended with Craig Dawson crossing from the right for Sessegnon to apply a calm finish.
The hosts were nearly guilty of undoing their good work immediately, as Arnautovic got away a curling shot that narrowly failed to find the target.
Yet West Brom continued to press, with Sessegnon heading straight at Thomas Sorensen and Mulumbu clattering the post a minute later.
It looked as though both teams would be content to settle for a point, but Adam then struck with a powerful effort from the edge of the box, ensuring Stoke leapfrogged Newcastle United into ninth spot.
