Striker Odemwingie's hopeful shot after 36 minutes opened the home side's account and the Nigerian added a second on the hour mark when he headed in an inviting Shane Long cross from close range.
West Brom have 17 points from 10 matches, level with fourth-placed Everton and seven points behind leaders Manchester United.
Southampton have collected four points, the same number as winless Queens Park Rangers, and are bottom due to their inferior goal difference.
West Brom have let points slip in their last two league matches against champions Manchester City and Newcastle United by conceding late goals but there were no mistakes this time against a Southampton side short on confidence.
Zoltan Gera spurned a great chance after 20 minutes when an Odemwingie shot went straight into his path but his touch from the six-yard line sent the ball sailing over the bar.
After Odemwingie's opener which flicked off Maya Yoshida and flew past unsighted goalkeeper Paulo Gazzaniga, Southampton were unlucky not to equalise courtesy of Rickie Lambert's neat snapshot that crashed against the crossbar early in the second half.
West Brom keeper Ben Foster made a good save to deny Southampton in stoppage time but that was as close as the visitors got on another tough night for the struggling south coast club.
In contrast, Odemwingie was delighted with his team's showing after West Brom's late defeats by City and Newcastle.
"This was a good response from a good team. We needed a bit of luck and it is simple, if you keep shooting you will score, we are happy with the three points," Odemwingie told Sky Sports.
