In a measurement-device-independent or quantum-refereed protocol, a referee can verify whether two parties share entanglement or Einstein-Podolsky-Rosen (EPR) steering without the need to trust either of the parties or their devices. The need for trusting a party is substituted by a quantum channel between the referee and that party, through which the referee encodes the measurements to be performed on that party's subsystem in a set of nonorthogonal quantum states. In this Letter, an EPR-steering inequality is adapted as a quantum-refereed EPR-steering witness, and the trust-free experimental verification of higher dimensional quantum steering is reported via preparing a class of entangled photonic qutrits. Further, with two measurement settings, we extract 1.106±0.023 bits of private randomness per every photon pair from our observed data, which surpasses the one-bit limit for projective measurements performed on qubit systems. Our results advance research on quantum information processing tasks beyond qubits.