We study a Majorana-carrying quantum wire, driven into a trivial phase by breaking the spatial inversion symmetry with a tilted magnetic field. Interestingly, we predict that a supercurrent applied in the proximate superconductor is able to restore the topological phase and therefore the Majorana end states. Using Abelian bosonization, we further confirm this result in the presence of electron-electron interactions and show a profound connection of this phenomenon to the commensurate-incommensurate transition in one-dimensional doped Mott insulators. These results have important applications in, e. g., realizing a supercurrent-assisted braiding of Majorana fermions, which proves highly useful in topological quantum computation with realistic Majorana networks. DOI: 10.1103/PhysRevB.87.060504