In fact, they looked the better side until West Ham opened the scoring on 12 minutes when Faubert crossed from the right and Carew was strong enough to hold off Matt Hill and find the bottom corner with his header.
But that opening goal was the signal for almost complete home dominance and the Hammers could have added a second almost immediately but Baldock was denied by Matt Gilks in the Blackpool goal.
Gilks was soon in action again, saving from Carew after a poor defensive error by Hill and then blocking a Carew shot with his legs.
Hammers goalkeeper Manuel Almunia was finally involved just before the interval but had no trouble holding a low shot by Jonjo Shelvey - and that was about as good as it got for the visitors.
The hosts' second goal arrived when Blackpool tried to play a high offside trap and Baldock duly converted after racing on to Matthew Taylor's header.
Another Hill mistake then gifted a third goal when he let the ball bounce in the area and Carew flicked the ball on to Baldock who tapped it over the line.
Collison completed the rout when his deflected volley from 12 yards easily beat Gilks, and only a superb save by the overworked keeper prevented Baldock completing his hat-trick.
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