We report a combined study of in-plane resistivity and thermopower of the pressure-induced heavy fermion superconductor CeAu2Si2 up to 27.8 GPa. It is found that thermopower follows a scaling behavior in T/T* almost up to the magnetic critical pressure pc ~ 22 GPa. By comparing with resistivity results, we show that the magnitude and characteristic temperature dependence of thermopower in this pressure range are governed by the Kondo coupling and crystal-field splitting, respectively. Below pc, the superconducting transition is preceded by a large negative thermopower minimum, suggesting a close relationship between the two phenomena. Furthermore, thermopower of a variety of Ce-based Kondo-lattices with different crystal structures follows the same scaling relation up to T/T* ~ 2.