We propose a diagnostic that can resolve the planet/binary degeneracy of central perturbations in caustic-crossing high-magnification microlensing events. The diagnostic is based on the difference in the morphology of perturbation inside the central caustics induced by a planet and a wide-separation binary companion. We find that the contours of excess exhibit a concentric circular pattern around the caustic center for the binary-lensing case, while the contours are elongated or off-centered for the planetary case. This difference results in the distinctive features of the individual lens populations in the residual of the trough region between the two peaks of the caustic crossings, where the shape of the residual is symmetric for binary lensing while it tends to be asymmetric for planetary lensing. We determine the ranges of the planetary parameters for which the proposed diagnostic can be used. The diagnostic is complementary to previously proposed diagnostics in the sense that it is applicable to caustic-crossing events with small finite-source effect.