High-voltage shunt reactors, serving as critical equipment for overvoltage suppression and reactive power compensation in power systems, require highly reliable inter-turn protection to ensure grid security. However, field operation has demonstrated that DC components or low-frequency components in the system can easily induce core saturation in reactors, leading to maloperation of traditional zero-sequence directional and impedance-based protection criteria. This paper analyzes the saturation mechanism of reactors and reveals that the flux superposition effect caused by DC bias and low-frequency oscillations is the root cause of protection maloperation. An anti-saturation protection method based on joint harmonic-DC component identification is proposed. This method employs an extreme-value envelope interpolation technique to extract low-frequency/DC components from current signals and dynamically adjusts the protection blocking threshold according to the ratio of these components to the fundamental frequency component. Simulations and field-recorded fault waveform validations confirm that the proposed method effectively distinguishes between reactor saturation and genuine inter-turn faults.