© 2018 authors. Published by the American Physical Society. We present the first limits on inelastic electron-scattering dark matter and dark photon absorption using a prototype SuperCDMS detector having a charge resolution of 0.1 electron-hole pairs (CDMS HVeV, a 0.93 g CDMS high-voltage device). These electron-recoil limits significantly improve experimental constraints on dark matter particles with masses as low as 1 MeV/c2. We demonstrate a sensitivity to dark photons competitive with other leading approaches but using substantially less exposure (0.49 g d). These results demonstrate the scientific potential of phonon-mediated semiconductor detectors that are sensitive to single electronic excitations.