We extend the Maxwell-Stefan (M-S) formulation of irreversible thermodynamics to multicomponent transport in mixed-matrix membranes (MMMs), using a simulation-based rigorous modeling approach (SMA) through finite-element method (FEM) solution of the three-dimensional (3-d) transport problem in full-scale MMMs. In the new approach, we generalize the dual-mode/partial immobilization (DM/PI) theory for the local permeability in glassy polymers to describe multicomponent permeation in pure glassy polymer membranes and MMMs, by reformulating the M-S constitutive equations in the Onsager formalism considering concentration-dependent transport diffusivities and non-uniform concentration gradients across the MMM. In this way, the new M-S formulation explicitly considers effects of intrinsic MMM features such as finite filler particle size and isotherm nonlinearity in the MMM constituent phases, as well as mixture-related effects, such as competitive adsorption and friction amongst permeants, on the calculation of the mixture fluxes (permeabilities). This is achieved without introduction of empirical fitting parameters in the MMM permeability calculation and only requiring single-gas experimental or simulation-based adsorption and permeation data on the individual MMM materials to predict the mixture perm-selectivity in the MMM as a whole. Further, we validate the new approach by using available experimental permeation data for the separation of an equimolar binary mixture of propylene (C3H6) and propane (C3H8) in ZIF-8/PIM-6FDA-OH MMMs, with the rigorous simulation results showing very good agreement with both experimental single and mixed-gas permeabilities and perm-selectivities.