We have investigated the field-temperature (H - T) diagram of the superconducting and pseudogapped states of Bi2Sr2CaCu2O8+y over a wide range of hole doping (0:10 < p < 0:225). Using interlayer tunneling transport in magnetic fields up to 60 T to probe the density-of states (DOS) depletion at low excitation energies we mapped the pseudogap closing field Hpg. We found that Hpg and the pseudogap onset temperature T* are related via a Zeeman relation gmB Hpg ~ kB T*, irrespective of whether the magnetic field is applied along the c-axis or parallel to CuO2 planes. In contrast to large anisotropy of the superconducting state, the field anisotropy of Hpg is due solely to the g-factor. Our findings indicate that the pseudogap is of singlet-spin origin, consistent with models based on doped Mott insulator.