Rub-impact is a common nonlinear fault of the rotor system, occurring in rotating machines with radial clearance between the rotor and the stator, which may lead to serious consequences. Since the vibration response of rotor rub-impact is shown as multicomponent with time-varying characteristics of undulatory instantaneous frequency, it is desired to exploit advanced signal processing methods for rub-related feature excavation and failure diagnosis under complex noise interferences, which is of crucial significance to ensure the stable and efficient operation of the whole unit. This paper concerns the processing of acceleration signals and proposes a novel intrawave frequency modulation detection approach for structural rotor rubbing diagnosis based upon targeted component extraction and stochastic resonance enhancement. First, the acquired vibratory acceleration signal is converted into displacement signal via a two-stage integration strategy. Next, to extract the rotating frequency component of high information clarity for further time–frequency analysis from the multicomponent signal, an especially designed improved variational mode decomposition method based on the modified target frequency index is put forward, and the instantaneous frequency of the objective component is estimated. Then, the optimum stochastic resonance is leveraged for intrawave frequency modulation enhancement. Finally, the rotor rub-related symptom can be distinctly revealed and the diagnostic procedure can be performed. The effectiveness and superiority of the proposed rotor rub-impact diagnosis approach are demonstrated through both simulations and experiments, indicating that it is suitable to be implemented in practical applications, with high noise-resistance ability, and can efficiently extract the potential characteristics of rotor rub-impact malfunction from multicomponent signals.