We report observations by Mars Global Surveyor (MGS) of thousands of peaked electron energy spectra similar to terrestrial auroral electrons. They are observed on the Martian nightside, near strong crustal magnetic sources. The spectra have peak energies ranging from 100 eV -- 2.5 keV, and fluxes near the peak are 10--10000 times higher than typical nightside spectra. They occur on magnetic field lines that connect the shocked solar wind to crustal magnetic fields, and on adjacent closed field lines. Their detection is directly controlled by the solar wind, suggesting that magnetic reconnection is required for their observation. We calculate that the most energetic distributions could produce atmospheric emission with intensity comparable to that recently reported from the Mars Express (MEX) spacecraft. Half of the most energetic examples occur during the passage of space weather events past Mars, suggesting that a disturbed plasma environment is favorable for electron acceleration along magnetic field lines.