The deliberate introduction of nonlinearities is widely used as an effective technique for the bandwidth broadening of conventional linear energy harvesting devices. This approach not only results in a more uniform behavior of the output power within a wider frequency band through bending the resonance response, but also contributes to energy harvesting from low-frequency excitations by activation of superharmonic resonances. This article investigates the nonlinear dynamics of a monostable piezoelectric harvester under a self-powered electromagnetic actuation. To this end, the governing nonlinear partial differential equations of the proposed harvester are order-reduced and solved by means of the perturbation method of multiple scales. The results indicate that, according to the excitation amplitude and load resistance, different responses can be distinguished at the primary resonance. The system behavior may involve the traditional bending of response curves, Hopf bifurcations, and instability regions. Furthermore, an order-two superharmonic resonance is observed, which is activated at lower excitations in comparison to order-three conventional resonances of the Duffing-type resonator. This secondary resonance makes it possible to extract considerable amounts of power at fractions of natural frequency, which is very beneficial in micro-electro-mechanical systems (MEMS)-based harvesters with generally high resonance frequencies. The extracted power in both primary and superharmonic resonances are analytically calculated, then verified by a numerical solution where a good agreement is observed between the results.