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The hosts could have fallen behind as early as the fourth minute had Steven Davis been able to keep his shot from outside the box on target.
Foster made a good save on the half-hour mark when he kept out Lambert's header from a Gaston Ramirez cross from close range.
Peter Odemwingie then came close twice to breaking the deadlock, before eventually putting West Brom ahead on 36 minutes, shooting with his left foot from outside the 18-yard box into the bottom left corner.
Odemwingie could have scored his second goal of the evening on the stroke of half-time, but failed to keep his shot on target.
Southampton started the second half the brighter of the two sides, as just three minutes into the restart Lambert rattled the home side's crossbar.
However, the visitors' hopes of getting a point from the Hawthorns evaporated on the hour mark, as Odemwingie headed home Long's cross from close range.
Five minutes later Gareth McAuley almost made it 3-0 to West Brom when he headed Gera's cross towards the Saints' goal, but failed to keep it on target.