Time-dependent density functional theory (TDDFT) is implemented in an all electron solid-state code for the case of fully unconstrained noncollinear spins. We use this to study intense, short, laser pulse-induced demagnetization in bulk Fe, Co, Ni and find that demagnetization can take place on time scales of <20 fs. It is demonstrated that this form of demagnetization is a two-step process: excitation of a fraction of electrons followed by spin-flip transitions mediated by spin-orbit coupling of the remaining localized electrons. We further show that it is possible to control the moment loss by tunable laser parameters, including frequency, duration, and intensity.