Goals from Kevin De Bruyne, David Silva, Gabriel Jesus and Yaya Toure set the seal on an emphatic triumph over the Hammers.
Pep Guardiola's men gained an early foothold when De Bruyne played a neat one-two on the counter with Jesus before finding the bottom corner of the hosts' net.
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And the second would follow minutes later when Leroy Sane's ball across the face of goal was smashed home by Silva to put City in control.
The visitors were running riot in the capital, with Jesus tapping home his first goal for the Club having been set up by Raheem Sterling before the break.
But the final word would go to Yaya Toure, who tucked home from the spot to add a fourth after Sterling had been brought down in the box by Jose Fonte.
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