Referee Mike Dean showed Feghouli a straight red card after the midfielder’s 15th-minute challenge on Phil Jones.
Replays showed it was more of a coming together between two players committed to winning the ball than a reckless tackle meant to cause harm.
Antonio Valencia was guilty of an astonishing miss for the visitors before Juan Mata scored from 10 yards after a clever pass by fellow substitute Marcus Rashford.
Zlatan Ibrahimovic was one of three players offside when he doubled the lead after Pedro Obiang’s clearance fell to Ander Herrera.
It was Jose Mourinho’s side’s sixth straight Premier League win and their seventh in all competitions.
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Dean at the centre of controversy – again
The Hammers have beaten Bournemouth, Sunderland, Burnley and Hull at home this season, yet their hopes of claiming a first major scalp at London Stadium were undone by the fastest sending off in the Premier League this season.
There is no doubt Feghouli lost control of the ball and deserved a booking for his challenge on Jones.
But Dean, who sent off Southampton’s Nathan Redmond in the 4-1 defeat by Tottenham on Wednesday, brandished a red card for the fifth time this season, much to the fury of West Ham boss Slaven Bilic.
Jones, who was clearly hurt and rolled over several times before receiving treatment, was booed by home fans for the rest of the game each time he touched the ball.
Feghouli is now set to miss his side’s FA Cup third-round home tie against Manchester City on Friday, while Hammers supporters showed their anger at the official by chanting ‘Mike Dean – it’s all about you’.
In the second half, Dean kept his cards in his pocket after Cheikhou Kouyate’s reckless challenge on Henrikh Mkhitaryan.
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