Faubert and Zamora combined excellently for the Hammers' first goal - the french winger crossing low for Jack Collison to get in a low shot from a tight angle.
Zamora's goals came when Kevin Keen opted to play a 4-5-1 system in the second 45, after pairing him with Zavon Hines in the first period.
On 58, Zamora found himself in an advanced position and holding off the attentions of two defenders the Hammers striker turned on a sixpence and fired past the goalkeeper.
His second was a product of Faubert, the winger's pacey charge along the right resulting in a fine cross which the 27 year old striker flicked beyond the young Birmingham keeper.
And to cap off an excellent night's work, it was Faubert once again who crossed in a glorious ball from the right for Zamora to rise and head home in the dying seconds.
Hammers:
Walker, Spence, Tomkins, N'Gala, Spector, Faubert, Stokes, Collison, Reid, Zamora, Hines (Stanislas 46, Hales 82)