In this article we provide explicit computations of the quantum corrections to the lightest CP-even Higgs Boson mass in the real version of the Minimal Supersymmetric Standard Model. We compute the contributions coming from the SUSY-QCD sector with a precision of three loops at order $O(\alpha_t\alpha_s^2)$. The renormalization procedure adopted is based on the dimensional reduction scheme in order to preserve supersymmetry to all perturbative orders. The calculation extends the region of validity of previous studies to the whole supersymmetric parameter space. The involved master integrals have been computed by exploiting new proposed approaches based on the dispersion relation techniques for the numerical calculation of three-loop vacuum integrals with arbitrary mass scales.