Beginning with cosmological initial conditions at z = 100, we simulate the effects of magnetic fields on the formation of Population III stars and compare our results with the predictions of Paper I. We use gadget-2 to follow the evolution of the system while the field is weak. We introduce a new method for treating kinematic fields by tracking the evolution of the deformation tensor. The growth rate in this stage of the simulation is lower than expected for diffuse astrophysical plasmas, which have a very low resistivity (high magnetic Prandtl number); we attribute this to the large numerical resistivity in simulations, corresponding to a magnetic Prandtl number of order unity. When the magnetic field begins to be dynamically significant in the core of the minihalo at z = 27, we map it onto a uniform grid and follow the evolution in an adaptive mesh refinement, MHD simulation in orion2. The nonlinear evolution of the field in the orion2 simulation violates flux-freezing and is consistent with the theory proposed by Xu & Lazarian. The fields approach equipartition with kinetic energy at densities ∼ 10 10 − 10 12 cm −3 . When the same calculation is carried out in orion2 with no magnetic fields, several protostars form, ranging in mass from ∼ 1 to 30 M ⊙ ; with magnetic fields, only a single ∼ 30 M ⊙ protostar forms by the end of the simulation. Magnetic fields thus suppress the formation of low-mass Pop III stars, yielding a top-heavy Pop III IMF and contributing to the absence of observed Pop III stars.