The September 10-12 Solar Energetic Particle (SEP) Event produced the strongest increase of the radiation environment measured by the Radiation Assessment Detector (RAD) on the surface of Mars since landing in August 2012. We report the details of the measurements of the energetic particle environment from RAD in Gale crater during this event. The SEP event increased the low-energy proton flux (below 100 MeV) by a factor of thirty, and the higher-energy proton flux by a factor of four, above pre-event levels. The 4He flux (below 100 MeV/nuc) rose by factors up to ten, and neutral particles by a factor of two above background. The increase started on September 10 around 19:50 UTC, peak-level fluxes were reached on the morning of September 11 and prevailed for about 10 hours before decreasing towards background levels. The onset of a Forbush decrease on September 13 decreased the proton flux below pre-event intensities.