We identify the phase boundary between spiral spin and ferromagnetic phases in Au$_2$Mn at a critical pressure of 16.4 kbar, as determined by neutron diffraction, magnetization and magnetoresistance measurements. The temperature-dependent critical field at a given pressure is accompanied by a peak in magnetoresistance and a step in magnetization. The critical field decreases with increasing temperature and pressure. The critical pressure separating the spiral phase and ferromagnetism coincides with the disappearance of the magnetroresistance peak, where the critical field goes to zero. The notable absence of an anomalous Hall effect in the the ferromagnetic phase is attributable to the high conductivity of this material.