Tony Pulis' side had the best of the first half and deserved to lead at the interval but a much-improved showing after the break earned the home side a draw at Upton Park
Tony Pulis' side went ahead in the 13th minute when Jon Walters completed a clever corner routine but the Hammers equalised after the interval through the defender, who directed a Gary O'Neil cross beyond Asmir Begovic.
Modibo Maiga and O'Neil replaced Matt Jarvis and Yossi Benayoun in Sam Allardyce's starting XI, while Pulis was handed a boost before the game as injury doubts Glenn Whelan, Jon Walters and Charlie Adam were all passed fit to play.
And it was Adam who had the first chance of the game when he connected with a Peter Crouch knock-down in the penalty area but volleyed tamely over the bar early on.
The pair combined again shortly afterwards to force George McCartney to concede a corner and, from the resulting delivery, Stoke went ahead as Walters' sharp run to the near post allowed him plenty of time and space to drill Glenn Whelan's precise cross beyond Jussi Jaaskelainen.
The visitors almost doubled their lead from another corner as Matthew Etherington found Robert Huth but Jaaskelainen pushed the centre-back's header away from danger.
West Ham finally mustered a response through Kevin Nolan, played in by Maiga, but the midfielder's powerful shot from close range was parried by Begovic.
Pulis made a substitution just after 30 minutes when Andy Wilkinson was forced off with an injury and replaced by Ryan Shotton.
Stoke continued to press, though, and were inches away from a second goal when Steven N'Zonzi let fly with a thunderous volley from 20 yards, which had Jaasklelainen well beaten but rattled against the bar.
Mohamed Diame skewed a long-range effort well wide just before the interval to sum up a disappointing half for the Hammers.
The hosts improved after the break and could have had an equaliser just a minute into the second half but Nolan tamely cushioned a well-placed McCartney cross into Begovic's chest.
West Ham were level moments later, however, as Diame bundled through the Stoke defence and fed O'Neil, whose pass left O'Brien with the simplest of finishes inside the six-yard box.
The Hammers continued to dominate and were nearly in front when Andy Carroll nodded Mark Noble's corner into Maiga's path but Begovic was equal to the striker's side-footed effort.
Stoke tried to change the game but West Ham went close again through O'Neil, whose shot from a narrow angle on the left-hand side curled beyond the far post and out of play.
Both sides made substitutions in search of a winner, Carlton Cole one of those introduced in place of the unhappy Carroll, but Begovic denied Nolan what would have been an open goal by blocking another McCartney delivery before saving a soft Winston Reid header to ensure that the Potters left Upton Park with a point.