Aims. Based on time series of high-resolution spectra, we investigate the oEA star (i.e., Algol-type eclipsing binary with an oscillating primary component) RZ Cas to derive precise system and atmospheric parameters and search for phases of rapid mass-transfer and its effects on various system parameters at different epochs of observations. Methods. We combine a variety of methods including the KOREL program to decompose the components of the spectra and determine the orbital solution, the SynthV program to analyze the disentangled spectra by computing synthetic spectra based on atmosphere models, and the newly developed program Shellspec07_inverse to compute optimized stellar parameters from composite line profiles at all orbital phases. Results. Based on spectra taken in 2006, the RZ Cas system can be modeled accurately by assuming that only two stars are present. For spectra acquired in 2001, we obtained an improved solution by adding a light attenuating accretion annulus surrounding the primary, but were unable to model remaining structures in the O–C value distribution. The primary of RZ Cas is a normal A-type star that shows no λ Boo signatures, both components have close to solar abundance. The derived mass of the primary and the separation of the components are slightly smaller than previously assumed. The effective temperature of the primary of 8900 K, is 300 K higher than derived before. The Roche-lobe-filling secondary is assumed to have a large cool spot on its surface pointing towards the primary. We confirm the increase in the orbital period by 2 s between years 2001 and 2006, but not the previously assumed decrease in the orbital radial velocity amplitudes. Conclusions. With the new Shellspec07_inverse program, we obtained precise stellar parameters of RZ Cas. Results clearly point to the occurrence of a transient phase of rapid mass transfer of RZ Cas in 2001, while in 2006 the system was in a quiet state.