The Potters reached the 40-point mark but they had no joy in an attacking sense as Saido Berahino was denied a first goal for the club by Winston Reid's fine block and Adrian's terrific save.
Southgate, who missed the Manchester derby on Thursday in favour of attending a rugby league game, witnessed Butland make just his second appearance since he fractured his ankle while on international duty last March.
Butland impressed with saves from Andre Ayew and Manuel Lanzini ahead of a possible Three Lions return in June.
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Stoke XI: Butland, Johnson, Muniesa, Shawcross, Martins Indi, Cameron, Whelan, Shaqiri, Allen, Arnautovic, Berahino
Subs: Bardsley, Pieters, Adam, Diouf, Crouch, Sobhi, Grant
West Ham XI: Adrian, Fonte, Reid, Collins, Fernandes, Kouyate, Nordtveit, Masuaku, Lanzini, Ayew, Calleri
Subs: Randolph, Cresswell, Feghouli, Snodgrass, Noble, Byram, Fletcher
Referee: Lee Probert
WHAT THEY SAID
Slaven Bilic: "A couple of games ago, [Stoke] had that game against Hull at home and then they were on 36 points and they needed to win that game.
"Now they are on 39 but knowing Mark Hughes, they will not be on a beach. I would like them to be, make no mistake.
"But I remember we played them the last game of last season and they were 10th and they could have been on the beach, big time, but no."
Mark Hughes: "It's a case of expectation. Since I've come here I've tried to raise expectations and for the most part we've matched the expectations of everybody at the club and the supporters.
"This year we've still got an opportunity to be in the top 10 but, for whatever reason, maybe the perception is that we haven't quite achieved what we were capable of."