We experimentally demonstrate the superior discrimination of separated, unentangled two-qubit correlated states using nonlocal measurements, when compared with measurements based on local operations and classical communications. When predicted theoretically, this phenomenon was dubbed ''quantum nonlocality without entanglement.'' We characterize the performance of the nonlocal, or joint, measurement with a payoff function, for which we measure 0.72 ᠰ.02, compared with the maximum locally achievable value of 2/3 and the overall optimal value of 0.75.