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.
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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