Application of a mild (60 mT), uniform magnetic field during short-term thermal treatment of kinetically retained, atomically disordered (paramagnetic) epsilon-MnAl was found to deliver a significant similar to 50 % increase in the formation of L1(0) atomically ordered (ferromagnetic) tau-MnAl product phase, compared to that produced by conventional (i.e., zero-field) annealing under identical thermal conditions. The magnetic field, applied in a passive closed-circuit configuration during annealing, induced significant changes in the structural, magnetic, and phase evolution of the material. Computational results based on electronic structure calculations demonstrate that the effective magnetic susceptibility of tau-MnAl is sensitive to the orientation, rather than the magnitude, of an applied magnetic field in the vicinity of the Curie temperature. The uniaxial magnetocrystalline anisotropy of the L1(0) structure is proposed to act as a filter for selective propagation of the population of tau-MnAl variants that are favorably aligned with the applied field. In this manner, crystallographic "gridlock" is alleviated that would otherwise arise from the coexistence of multiple, energetically equivalent tau-phase variants within the parent epsilon-phase matrix. These results confirm that static, low-magnitude magnetic field annealing is able to accelerate L1(0) atomic ordering in the MnAl system and likely can exert similar influences in relevant magnetic systems, facilitating efficient tailoring of structure-sensitive magnetic properties for the manufacture of magnetic materials.