The Nigerian netted in each half to hand Mark Hughes' men their second win in three games after Andy Carroll had opened the scoring with his first goal of the season
Andy Carroll's first Premier League goal of the season had put Sam Allardyce's men in front after five minutes but Odemwingie ensured the Potters were level heading into the break.
After the restart, Marko Arnautovic put Mark Hughes' side ahead before the Nigeria forward wrapped up the victory with 11 minutes remaining.
West Ham had two penalty appeals turned away and a Kevin Nolan goal disallowed but have slipped to consecutive Premier League defeats for the first time since December.
|BATTLE AT THE BOTTOM
16. West Brom
17. Crystal Palace
The visitors made a strong start to the match with an early goal as Carroll rose above Asmir Begovic and Peter Crouch to head home Mark Noble's cross.
A minute later, Stoke were denied an equaliser after an excellent save from Adrian.
Neat interplay between Crouch and Odemwingie created an opening for Stephen Ireland, who replaced the suspended Jonathan Walters, but his first-time effort was tipped wide by the Spanish goalkeeper.
The game settled down after a frantic start with both sides enjoying good periods of possession before Stoke pulled level after 32 minutes through Odemwingie.
Crouch met a corner from Ireland, but his header was tipped onto the bar by Adrian. The striker reacted quickly to get the rebound and his acrobatic flick struck Odemwingie on his shoulder on its way over the line.
Having restored parity, Stoke should have gone into the break with an advantage as a neat passing move saw Arnautovic release Ireland in behind the defence, but his close-range effort was straight at Adrian and allowed him to make an easy save.
After a sluggish opening to the second half, West Ham had the ball in the net just after the hour, only for an offside flag to rule it out.
Begovic again failed to claim a ball into the penalty area, his punch dropped straight to Antonio Nocerino and his touch over the goalkeeper fell to Nolan, who promptly fired into the open net, but his effort was chalked off.
After surviving West Ham's pressure, Stoke grew in stature and took the lead with Arnautovic's third goal for the club.
Another good move from Mark Hughes' men saw Odemwingie find the Austrian on the edge of the penalty area, he bundled his way past a defender and fired low past Adrian – although the goalkeeper should have done better.
West Ham saw two penalty shouts turned away before Odemwingie sealed the win with 11 minutes left with an emphatic strike from the edge of the penalty area.