This paper presents a new method to diagnose rotor faults in operating three-phase induction motors under the presence of time-varying loads. The proposed diagnostic strategy relies on a combined analysis of the amplitude and phase spectra of the instantaneous active and reactive powers of the motor, and allows to discriminate the effects introduced by a rotor fault from the ones caused by an oscillating load torque, even when these phenomena occur simultaneously. A theoretical analysis carried out using a linearized model of the induction motor in a synchronous reference frame, complemented with several simulation and experimental results, confirms the validity of the proposed diagnostic approach.