We report quantitative analysis of nonequilibrium spin injection from Ni contacts to the octanethiol molecular spintronic system. Our calculation is based on carrying out density functional theory within the Keldysh nonequilibrium Green's function formalism. The first principles results allow us to establish a clear physical picture on how spins are injected from the Ni contacts through the Ni-molecule linkage to the molecule, why tunnel magnetoresistance is rapidly reduced by the applied bias in an asymmetric manner, and to what extent ab initio transport theory can make quantitative comparisons to the corresponding experimental data. We found that extremely careful sampling of the two-dimensional Brillouin zone of the Ni surface is crucial for accurate results.