AnoptimalcontrolproblemforacontrolledbackwardstochasticpartialdifferentialequationintheabstractevolutionformwithaBolzatypeperformancefunctionalisconsidered.Thecontroldomainisnotassumedtobeconvex,andallcoefficientsofthesystemareallowedtoberandom.Avariationalformulaforthefunctionalinagivencontrolprocessdirectionisderived,bytheHamiltonianandassociatedadjointsystem.Asanapplication,aglobalstochasticmaximumprincipleofPontrayginstypefortheoptimalcontrolsisestablished.