The Saints played their part in a lively match at The Hawthorns but struggled to cope with a vibrant Baggies attack, led by Shane Long and Odemwingie, whose brace took the hosts up to fifth.
Southampton made a bright start to the contest and Steve Davis fired high and wide from distance before Rickie Lambert tested Ben Foster with a low drive.
But the hosts then enjoyed a period of strong pressure and Zoltan Gera should probably have done better than side-foot Odemwingie's cross-shot over the bar from close range.
Long then tried to curl one into the top corner, while Lambert put a header straight at Foster from a Gaston Ramirez cross at the other end, as the game opened up.
The Baggies were now looking really dangerous, however, and claimed a somewhat fortuitous lead when Youssouf Mulumbu found Odemwingie (36) and, after possibly controlling the ball with his arm, he unleashed a powerful shot from the edge of the box which hit Maya Yoshida's leg and flew past Paulo Gazzaniga.
The lead was almost doubled just before half-time but Gazzaniga, starting in place of Artur Boruc, did well to deny Long after a surging run into the box by the striker and the lively Odemwingie's follow-up effort hit Morgan Schneiderlin and bounced away to safety.
Southampton came within inches of restoring parity after the break when Jay Rodriguez's cross ricocheted around before falling kindly for Lambert, who stroked a half-volley against the bar.
The visitors continued to probe for an opening but then fell further behind to a brilliant counter-attacking goal from the Baggies, Long racing down the left to latch onto a long pass from Liam Ridgewell and then cutting inside, before whipping over a superb cross which Odemwingie (60) headed home from close range.
And West Brom came very close to adding a third but Chris Brunt arrived at the back post to volley just wide of the target after good work from Romelu Lukaku.The Saints almost grabbed a late consolation but Yoshida headed wide from a corner and Foster foiled Adam Lallana in stoppage-time.
|West Bromwich Albion||Team Statistics||Southampton|
|1||1st Half Goals||0|
|3||Shots on Target||3|
|9||Shots off Target||5|
|54||1st Half Poss.||46|
|34.1||2nd Half Poss.||65.9|