Reliable long-term creep rupture life prediction of high-temperature materials demands a deep understanding of rupture-controlling mechanisms. Conventional analytical models for creep rupture extrapolation rely heavily on experimental data and adjustable parameters, potentially neglecting the critical failure mechanisms. This study employs fundamental creep models for HR3C(25Cr20NiNbN) austenitic steels, incorporating ductile and brittle creep mechanisms with well-defined physical parameters and no adjustable parameters. The ductile creep models account for dislocation hardening, precipitation hardening, solid solution hardening, and stacking faults, while the brittle creep models in addition consider creep cavitation along sliding grain boundaries. Key physical parameters are derived as follows: precipitate evolution is simulated using thermodynamic computations and validated against experiments, while high-temperature elastic properties and atomic-size misfit are determined through first-principles calculations, with lattice vibrations incorporated via the quasi-harmonic Debye model. By combining first-principles and thermodynamic calculations, the mechanism-based fundamental models successfully predict the creep rupture strength of HR3C quantitatively.