Saints had to play for the majority of the second half with 10 men after Wanyama's dismissal - his third of the season - for a tackle on Dimitri Payet
But West Ham could not find a way past a Saints rearguard which has now kept five consecutive clean sheets, with goalkeeper Fraser Forster yet to concede in seven and a half hours since he returned from a long-term injury
In truth Forster had little to do, although when he was called upon to keep out a powerful Winston Reid header, he was equal to the task
West Ham keeper Adrian was straight into the action, by contrast, and he pulled off a fine point-black save to keep out Cedric Soares' header from Shane Long's cross.
Yoshida's goal came in the ninth minute after t he visitors failed to deal with a corner
Wanyama charged into the area and prodded the ball into the path of Yoshida to sweep past Adrian from close range
West Ham claimed they should have had a penalty when Yoshida clipped Enner Valencia's heels but referee Mark Clattenburg was not convinced.
Forster came to Saints' rescue on the half-hour mark with a superb reflex save, palming out Reid's goalbound header
New Zealand defender Reid then glanced another header narrowly over the crossbar from Payet's corner
Payet was starting to exert his influence after the break when, in the 53rd minute he skipped away from Wanyama in the centre-circle only to be chopped down from behind by Saints' midfield enforcer
The challenge enraged Hammers boss Slaven Bilic, who had seen his key playmaker sidelined for three months by a similar tackle by Everton's James McCarthur earlier in the season
Clattenburg took his time to make a decision, initially appearing to reach for a yellow card, but he eventually settled on a straight red as the former Celtic midfielder pleaded his innocence
Long could have doubled Saints lead just after the hour when James Collins misjudged Forster''s long clearance only to blaze his shot over the crossbar
West Ham's new signing Emmanuel Emenike almost made a name for himself moments after coming on as a substitute, but he headed Sam Byram's cross wide
In stoppage-time West Ham appealed for another penalty after Collins' shot hit Jose Fonte's arm, but it was not to be their day
TWEET OF THE MATCH
Former Southampton forward Matt Le Tissier (@mattletiss7): Anyone else get the feeling Mark Clattenburg doesnt like @SouthamptonFC much?
RATINGS
Southampton
Fraser Forster: 7 (out of 10)
Ryan Bertrand: 7
Jose Fonte: 7
Virgil van Dijk: 8
Maya Yoshida: 7
Cedric Soares: 7
Jordy Clasie: 6
Victor Wanyama: 6
Sadio Mane: 6
Shane Long: 7
Graziano Pelle: 6
Subs
Oriol Romeu: 5
Charlie Austin: 6
James Ward-Prowse: 5
West Ham
Adrian: 6
Aaron Cresswell: 6
James Collins: 6
Winston Reid: 6
James Tomkins: 6
Alex Song: 5
Mark Noble: 6
Dimitri Payet: 6
Victor Moses: 5
Enner Valencia: 6
Michail Antonio: 5
Subs
Andy Carroll: 5
Sam Byram: 6
Emmanuel Emenike: 6
STAR MAN
Virgil van Dijk: The Saints defender stood firm as West Ham poured forward looking for a late equaliser
Got a head to everything they threw at him.
MOMENT OF THE MATCH
Fraser Forster has still not let in a goal since he returned from injury, and he made a stunning point-black save from Reid's header to preserve that record.
VIEW FROM THE BENCH
Saints once again started with their three centre-halves at the back, and it is still paying off
West Ham started with four wingers and no recognised striker
It didn't pay off
MOAN OF THE MATCH
Referee Mark Clattenburg appeared to initially reach for a yellow card to show to Victor Wanyama
Was his decision swayed by the West Ham players who surrounded him?
Source : PA
Source: PA