We report Coulomb mediated hybridization of excitonic states in optically active InGaAs quantum dot molecules. By probing the optical response of an individual quantum dot molecule as a function of the static electric field applied along the molecular axis, we observe unexpected avoided level crossings that do not arise from the dominant single-particle tunnel coupling. We identify a new few-particle coupling mechanism stemming from Coulomb interactions between different neutral exciton states. Such Coulomb resonances hybridize the exciton wave function over four different electron and hole single-particle orbitals. Comparisons of experimental observations with microscopic eight-band k·p calculations taking into account a realistic quantum dot geometry show good agreement and reveal that the Coulomb resonances arise from broken symmetry in the artificial semiconductor molecule.