Villa's cause was made immeasurably more difficult after 17 minutes when Jordan Ayew had a moment of madness and swung his elbow into the face of West Ham's Aaron Cresswell, earning himself a straight red card.
It took West Ham until the 58th minute, however, to break the deadlock with Antonio guiding a header into the net following an excellent crossfield ball from Mark Noble.
They doubled the lead when Kouyate lifted the ball into the roof of the net after 85 minutes.
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West Ham are sixth on 39 points while Villa stay rooted to the foot of the table on 13.
(Reporting by Toby Davis; editing by Martyn Herman)
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