There appeared little danger when Jonathan Walters pumped a harmless ball into the box but Foster and Tamas allowed Shotton to nip in and score with only a minute remaining of normal time.
The goal earned unbeaten Stoke their first league win of the campaign, after two draws, and means Albion have lost their opening three matches.
Until then it looked as if Stoke goalkeeper Asmir Begovic's superb save from Shane Long would be the most notable action.
The Bosnian international's reflex first-half stop denied summer signing Long a third goal in three games.
West Brom were the better side in the first half, with captain Chris Brunt's crosses a constant threat, but Stoke weathered the storm and Shotton's late strike settled the match in their favour.
Jonathan Woodgate produced another fine defensive display for the Potters after his move from Tottenham.
In midfield West Brom's Youssouf Mulumbu and Stoke's Dean Whitehead took the honours.
The first decent opportunity fell to West Brom after good play by Somen Tchoyi who retained his place after Peter Odemwingie suffered a recurrence of his ankle problem.
He used his physical strength to hold off the challenge of Ryan Shawcross and his cross was met by Brunt but the Albion skipper sent his header wide.
Paul Scharner escaped the marking of Woodgate to connect with a Brunt free-kick but his powerful header was directed straight at Begovic.
A superb save from Begovic prevented West Brom taking the lead after 12 minutes.
Tchoyi delivered a testing cross from the left flank and Long's bullet header from six yards drew a fine stop from Begovic.
West Brom were looking the more likely to break the deadlock and Mulumbu volleyed over from the edge of the box after Woodgate had half-cleared a Nicky Shorey centre.
The home side continued to look more threatening and won a free-kick just outside the Stoke box after Walters fouled Tchoyi.
Brunt's free-kick completely wrong-footed Begovic but flew inches wide.
The visitors were forced to make a change after 36 minutes when Marc Wilson limped off with what appeared to be a hamstring injury and was replaced by Andy Wilkinson.
He slotted in at right-back with Huth reverting to the left-back role vacated by Wilson.
Stoke created their first worthwhile opening of the game after 49 minutes.
Glenn Whelan took a pass from Walters in his stride and his low shot flew just wide.
Chances were at a premium with play becoming more scrappy.
Tchoyi found himself in space 20 yards out after good play by Shorey with the overlapping Scharner completely unmarked to his right.
But Tchoyi went for the spectacular goal himself and curled his shot past the post.
Brunt was substituted after 65 minutes and replaced by Jerome Thomas.
Etherington made way for Danny Pugh a minute later, with Shotton taking over from Jermaine Pennant with 15 minutes remaining.
There was a rare moment of excitement when Tchoyi volleyed just wide after Scharner had nodded a cross from Steven Reid invitingly into his path.
It was Tchoyi's last action after a disappointing second-half performance before he was replaced by Marc-Antoine Fortune.
West Brom forced three successive corners in a late spell of pressure but could not find a way through - and then came Shotton's decisive intervention.