Striker Jake Jervis scored the only goal seven minutes into the match at Damson Park on Monday evening.
This was Blues' third consecutive Barclays Premier Reserves League South victory under new coach Malky Thomson.
Blues Res: Butland, Wilson, Timmins, Kerr, Preston, Mutch, Hubbins (Hronec, h/t), Sammons, Jervis (McPike, 76), Shroot, Asante (Bogle, 79). Subs not used: Osturk, Luke Rowe.
Stoke Res: St Louis-Hamilton, Cohen, Wedderburn, Pugh, Cort, Davies, Lund, Amdy Faye, Marshall, Kitson, Wint (Moult, 55). Subs not used: McDonald, Parton, Urwin.