Jake Jervis opened the scoring for Blues 16 minutes into the match at Damson Park and Damien Johnson gave new second string coach Malky Thomson's side a 2-0 first half lead just after the half-hour mark.
The Hammers pulled one goal back six minutes after the break with a Frank Nouble spot kick but Blues held on to take maximum points to lift themselves off the foot of the Barclays Premier Reserves League South table.
Blues Res: Doyle, Wilson, Espinoza, Queudrue, Vignal, O'Shea, Carsley, Damien Johnson, Fahey, Jervis, McSheffrey. Subs: Butland, Jacob Rowe, Shroot, Sammon, Bogra.
West Ham Res: Kurucz, Eyjolfsson, N'Gala, Daprela, Ferrari, Payne, Dyer, Kearns, Nouble, Dixon, Edgar. Subs: Loveday, Modelski, Zola, Wearen, Grasser, Montano.