This paper proposes a novel inerter-based component dynamic vibration absorber, namely, electromagnetic resonant shunt tuned mass-damper-inerter (ERS-TMDI). To analyze the performances of the ERS-TMDI, the combined ERS-TMDI and a single degree of freedom system are developed. The h(2) norm performances of the ERS-TMDI, whose aim is to minimize the root mean square (RMS) value of structure damage under random ground acceleration excitation, are introduced in comparison with the energy-harvesting series electromagnetic tuned mass dampers (ERS-TMDs), tuned mass-damper-inerter (TMDI) and the classical tuned mass damper (TMD). The closed-form solutions, including the optimal mechanical tuning ratio, the optimal electrical damping ratio, the optimal electrical tuning ratio and the optimal electromagnetic mechanical coupling coefficient, are obtained. It is shown that the ERS-TMDI is superior to both the classical TMD and the ERS-TMD systems for protection from structure damage. Specifically, from the frequency-domain analyses, a case study is performed to illustrate the effectiveness, robustness of the ERS-TMDI and the sensitivity to the parameter changes. From the time-domain analyses, four types of earthquakes are studied to demonstrate the performances of vibration suppression.