In this study, the problem of magnetohydrodynamics (MHD) mixed convection of lid-driven cavity with a triangular-wave shaped corrugated bottom wall filled with a non-Newtonian power-law fluid is numerically studied. The bottom corrugated wall of the cavity is heated and the top moving wall is kept at a constant lower temperature while the vertical walls of the enclosure are considered to be adiabatic. The governing equations are solved by the Galerkin weighted residual finite element formulation. The influence of the Richardson number (between 0.01 and 100), Hartmann number (between 0 and 50), inclination angle of the magnetic field (between 0 deg and 90 deg), and the power-law index (between 0.6 and 1.4) on the fluid flow and heat transfer characteristics are numerically investigated. It is observed that the effects of free convection are more pronounced for a shear-thinning fluid and the buoyancy force is weaker for the dilatant fluid flow compared to that of the Newtonian fluid. The averaged heat transfer decreases with increasing values of the Richardson number and enhancement is more effective for a shear-thickening fluid. At the highest value of the Hartmann number, the averaged heat transfer is the lowest for a pseudoplastic fluid. As the inclination angle of the magnetic field increases, the averaged Nusselt number generally enhances.