The Baggies jump ahead of Tottenham and Arsenal in the table with a competent display against the basement club, as the Nigerian striker helped himself to two goals.
Despite the end result, it was the Saints who started the brighter of the two, and Rickie Lambert forced Ben Foster into a save with a first-time shot on the angle.
West Brom's first real chance of the game came after 19 minutes when Odemwingie burst down the right-hand channel before cutting in on his left and rifling a shot towards goal. The ball was going wide but was helped on its way by Zoltan Gera, who could only send it over the bar.
Long's first-time effort from a Youssuf Mulumbu pass flew into the crowd and Claudio Yacob dragged an effort wide as the game started to open up a little.
There was action at both ends of the pitch in the space of 30 seconds, with Foster comfortably saving Lambert's header from a Gaston Ramirez cross before quickly throwing the ball out to Odemwingie. The Nigerian burst down the right-hand channel before cutting in on his left and unleashing a fizzing shot that went just wide of the post.
Having just gone close with a left-footed drive, it was no surprise when Odemwingie finally did score by doing almost exactly the same again after 36 minutes. He collected Mulumbu's pass before taking a touch and driving in from 20 yards out. The ball took a deflection of the unfortunate Jose Fonte, which took it past Paulo Gazzaniga and into the bottom corner.
The Saints' goalkeeper produced a fine save at the feet of Long when the Republic of Ireland striker was allowed a free run into the box. The rebound fell to Odemwingie but his shot was blocked wide.
Southampton, which fell to 1-8-1 with the loss and has a league-worst -14 goal differential, went close a few minutes after the restart, Rickie Lambert smashing the bar on the half-volley as the Saints went looking for the equalizer.
But it was the Baggies who got their noses further in front with a quick, counter-attacking move. Liam Ridgewell booted the ball down the channel, Long ran onto it and whipped an inviting cross into the box which Odemwingie headed in from close range on the hour mark.