We study vanadium spinels AV2O4 (A = Cd,Mg) in pulsed magnetic fields up to 65 T. A jump in magnetization at μ0H≈40 T is observed in the single-crystal MgV2O4, indicating a field induced quantum phase transition between two distinct magnetic orders. In the multiferroic CdV2O4, the field induced transition is accompanied by a suppression of the electric polarization. By modeling the magnetic properties in the presence of strong spin-orbit coupling characteristic of vanadium spinels, we show that both features of the field induced transition can be successfully explained by including the effects of the local trigonal crystal field.