We study the nonequilibrium transport of two-dimensional electrons through a periodic potential. Our samples are fabricated using the cleaved-edge overgrowth technique to provide a vertical field-effect transistor with an undoped GaAs/AlGaAs superlattice channel orthogonal to the current flow. We find a pronounced negative differential resistance, the magnitude of which increases with increasing modulation strength. The data are qualitatively consistent with the Esaki–Tsu transport model in minibands, which we calculate for the given samples. We emphasize the significance of the two-dimensionality of the electron system and the gate to inhibit domain formation. Weak features in the source-drain current are attributed to Bloch-phonon resonances.