By exchanging the internal energy between coupled vibration modes, internal-resonance-based energy harvesters may provide an effective solution to broadening and enhancing bandwidth and power performance in dealing with natural vibration sources. With the development of piezoelectric-based transducers, thickness and face shear coefficients in proper piezoelectric elements can also generate power output from shear deformation on the core vibrating elements. However, in most cantilever-based energy harvesters that focused on bending modes, the shear responses were neglected. In this paper, we present an internal-resonance-based piezoelectric energy harvester with three-dimensional coupled bending and torsional modes, for the first time. The fine-tuned system leverages a two-to-one internal resonance between its first torsion and second bending modes to enhance the power output with piezoelectric effects. The dynamic behavior implies the coexistence of in-plane and out-of-plane motions under a single excitation frequency, and the corresponding strain changes in the bending and shear directions are captured by bonded piezoelectric transducers. Dependence between excitation levels and the internal-resonance phenomenon is justified as a critical system parameter study; the results also indicate that an intriguing non-periodic region exists near the center frequency. The outcomes of this study feature a multi-directional and multi-modal energy harvester that displays rich dynamic behaviors. The operational bandwidth is promising for broadband energy harvesting, and the output voltage is enhanced by capturing both in-plane and out-of-plane motions at the same time.