Recent advances in computational petrological modeling provide accurate methods for computing seismic velocities and density within the lithospheric and sub-lithospheric mantle, given the bulk composition, temperature, and pressure within them. Here, we test an integrated geophysical-petrological inversion of Rayleigh- and Love-wave phase-velocity curves for fine-scale lithospheric structure. The main parameters of the grid-search inversion are the lithospheric and crustal thicknesses, mantle composition, and bulk density and seismic velocities within the crust. Conductive lithospheric geotherms are computed using P-T-dependent thermal conductivity. Radial anisotropy and seismic attenuation have a substantial effect on the results and are modeled explicitly. Surface topography provides information on the integrated density of the crust, poorly constrained by surface waves alone. Investigating parameter inter-dependencies, we show that accurate surface-wave data and topography can constrain robust lithospheric models. We apply the inversion to central Mongolia, south of the Baikal Rift Zone, a key area of deformation in Asia with debated lithosphere-asthenosphere structure and rifting mechanism, and detect an 80-90 km thick lithosphere with a dense, mafic lower crust and a relatively fertile mantle composition (Mg# < 90.2). Published measurements on crustal and mantle Miocene and Pleistocene xenoliths are consistent with both the geotherms and the crustal and lithospheric mantle composition derived from our inversion. Topography can be fully accounted for by local isostasy, with no dynamic support required. The mantle structure constrained by the inversion indicates no major thermal anomalies in the shallow sub-lithospheric mantle, consistent with passive rifting in the Baikal Rift Zone.