We obtained time-resolved optical photometry and spectroscopy of the nova-like variable KR Aurigae in the low state. The spectrum reveals a DAB white dwarf (WD) and a mid-M dwarf companion. Using the companion star's i-band ellipsoidal modulation we refine the binary orbital period to be P = 3.906519 ± 0.000001 h. The light curve and the spectra show flaring activity due to episodic accretion. One of these events produced brightness oscillations at a period of 27.4 min, that we suggest to be related with the rotation period of a possibly magnetic WD at either 27.4 or 54.8 min. Spectral modelling provided a spectral type of M4-5 for the companion star and T1 = 27,148 ± 496 K, log g=8.90 ± 0.07, and log (He/H)= -0.79+0.07-0.08 for the WD. By simultaneously fitting absorption- and emission-line radial velocity curves and the ellipsoidal light curve, we determined the stellar masses to be M1 = 0.94+0.15-0.11 M☉ and M2 = 0.37+0.07-0.07 M☉ for the WD and the M-dwarf companion, respectively, and an orbital inclination of 47+1°-2°. Finally, we analyse time-resolved spectroscopy acquired when the system was at an i-band magnitude of 17.1, about 1.3 mag brighter than it was in the low state. In this intermediate state, the line profiles contain an emission S-wave delayed by ≃0.2 orbital cycle relative to the motion of the WD, similar to what is observed in SW Sextantis stars in the high state.