A small magnetic field is found to enhance relaxation processes in a superconductor, thus stabilizing superconductivity in nonequilibrium conditions. In a normal-metal (N)/insulator/superconductor (S) tunnel junction, applying a field of the order of μT leads to significantly improved cooling of the N island by quasiparticle (QP) tunneling. These findings are attributed to faster QP relaxation within the S electrodes as a result of enhanced QP drain through regions with a locally suppressed energy gap due to magnetic vortices in the S leads at some distance from the junction.