The Nigerian striker cancelled out Andy Carroll's opener when he deflected a Peter Crouch strike into the back of the net and went on to score his side's third after 79 minutes with a powerful effort.
Stoke found themselves behind after five minutes when Carroll headed home from close range, but Odemwingie's brace either side of Marko Arnautovic's effort turned the Premier League clash around.
West Ham had two penalty appeals turned away and a Kevin Nolan goal disallowed as Sam Allardyce's men slumped to a second consecutive defeat, while Stoke boosted their survival chances.
The visitors made a solid start to the match with a goal after five minutes as Carroll, who got the nod ahead of Carlton Cole in attack, rose above everyone to head home.
Mark Noble delivered a perfect ball to the back post towards the striker and Asmir Begovic came to collect, but Carroll beat him and Crouch to the ball and powered his header into the empty net.
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 left-wing 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 ahead 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 start 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.
