After a storming start, the Saints forged ahead after just eight minutes when their Japanese defender Maya Yoshida prodded home Saido Mane's delivery from close range.
When Yoshida stood on Enner Valencia's foot, the Hammers' penalty claims were waved away by Mark Clattenburg but the referee offered them a lifeline nine minutes after the break when showing Wanyama a straight red for a lunging challenge on Dimitri Payet, whose theatrical howls helped seal his fate.
Southampton were under the cosh for much of the rest of the game but held out to record their fifth consecutive clean sheet in the league and inflict only the Hammers' second defeat in 14 League and Cup games.
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(Reporting by Ian Chadband, editing by Pritha Sarkar)
