The fixed pivot technique of Kumar and Ramkrishna (Chem. Eng. Sci. 1996, 51(8), 1311-1332), originally derived for one-dimensional systems, is extended to simulate two-component aggregation processes. By following this approach, it is possible to design a numerical method that guarantees internal consistency with regard to certain moments of the distribution, while using arbitrary Cartesian grids. Focus is put on achieving internal consistency with respect to the number of particles and the mass of each component, although other moments may be considered if desired. The potentialities and limitations of the technique are evaluated by comparing the numerical solutions against available analytical solutions. This comparison reveals that the proposed method is rather accurate, except in the front region, which shows some smearing. The accuracy, internal consistency, and computational efficiency of this numerical method should make it a valuable tool for simulating two-component aggregation.