This paper presents an analytical solution of Reynolds' equation for the hydrodynamic lubrication flow in a parallel plate-on-annulus configuration of a conventional rotational rheometer. In this triborheometrical configuration originally proposed by Kavehpour and McKinley [Tribol. Lett. 17, 327-335 (2004)], the shearing surfaces are pushed together by an externally applied normal force. This solution predicts quantitatively how lubrication forces are enlarging the gap h between the surfaces with increasing angular velocity Omega, depending solely on the unavoidable misalignment alpha of the surfaces. The predicted gap evolution as well as the predicted scaling of the shear stresses sigma(21) similar to Omega(2/3) for the hydrodynamic flow regime for Newtonian fluids are experimentally verified with polydimethyl siloxane melts of different viscosities. The analysis is extended to power-law fluids, and the consistency of theoretical predictions and experimental observation was shown for a strongly shear thinning polyisobutylene in pristane solution. Finally, it is shown that for a known misalignement alpha of the triborheometrical configuration the setup can be used to determine the high shear viscosity of an unknown sample, in the current setup up to shear rates of 10(5) s(-1). (C) 2013 The Society of Rheology. [http://dx.doi.org/10.1122/1.4766364]