Sergio Aguero had put the hosts ahead when he finished off a flowing move that involved Samir Nasri playing one-twos with both Yaya Toure and David Silva before providing the cross for the City striker's 15th goal of the season.
Toure doubled the advantage with a marvellous goal after the break, making room for himself on the angle of the penalty area before firing superbly into the top corner.
West Ham did improve after the interval, although Andy Carroll's contribution once again raised talk of the present loan deal from Liverpool turned into a permanent arrangement.
"We will find out at the end of the season," said Allardyce. "There is a lot to do obviously, between ourselves, Liverpool and Andy.
"But he has scored again hasn't he? That is six in 10 now."
- Sports & Recreation
- Yaya Toure
- Samir Nasri
- David Silva
- Sergio Aguero
- Andy Carroll