To address the low energy harvesting efficiency of conventional energy harvesters under low-frequency broadband vibration excitation, an internal resonance piezoelectric energy harvester with time-varying potential wells (TI-PEH) was proposed. TI-PEH consists of a piezoelectric cantilever beam, an inverted auxiliary beam, a magnetic pendulum, limiters, a magnet at the free end of the inverted auxiliary beam, and a mass block. The elastically supported magnet is introduced to create time-varying potential wells, enhancing the coupling effects between internal resonance and nonlinear magnetic interactions. The experimental results show that within the range of 2~5 Hz, compared with the traditional structure, the maximum root mean square (RMS) voltage of the TI-PEH under 0.1 g excitation intensity is increased by 276%. Under random excitation conditions, the coupling effect between the time-varying potential well and the internal resonance can significantly enhance the output performance of the TI-PEH. Furthermore, stiffness reduction of the auxiliary beam enables the TI-PEH's operational bandwidth to shift toward lower frequencies, demonstrating superior energy harvesting performance in ultralow-frequency vibration environments.