A new method is presented that improves the supermolecular second-order Møller-Plesset (MP2) method for dimer systems with strong dispersion interactions while preserving the generally good performance of MP2 for other types of intermolecular interactions, e.g., hydrogen-bonded systems. This is achieved by adding a correction term to the supermolecular MP2 energy that is determined using time-dependent density functional (TDDFT) response theory and that accounts for the error of the dispersion energy contained in the supermolecular MP2 method. It is shown for the S22 database set of noncovalent complexes and some potential energy curves of noncovalent bound aromatic dimers that the approach gives strong improvements over MP2 if compared to coupled-cluster singles, doubles, and perturbative triples (CCSD(T)) reference energies. An efficient computer implementation of the method is presented that is shown to scale only with the fourth power of the system size and thus leads only to a slightly higher computational cost than that of the supermolecular MP2 itself.