Topological insulators offer significant potential to revolutionize diverse fields driven by nontrivial manifestations of their topological electronic band structures. However, the realization of superior integration between exotic topological states and superconductivity for practical applications remains a challenge, necessitating a profound understanding of intricate mechanisms. Here, we report experimental observations for a novel superconducting phase in the pressurized second-order topological insulator candidate Ta2Pd3Te5, and the high-pressure phase maintains its original ambient pressure lattice symmetry up to 45 GPa. Our in situ high-pressure synchrotron X-ray diffraction, electrical transport, infrared reflectance, and Raman spectroscopy measurements, in combination with rigorous theoretical calculations, provide compelling evidence for the association between the superconducting behavior and the densified phase. The electronic state change around 20 GPa was found to modify the topology of the Fermi surface directly, which synergistically fosters the emergence of robust superconductivity. In-depth comprehension of the fascinating properties exhibited by the compressed Ta2Pd3Te5 phase is achieved, highlighting the extraordinary potential of topological insulators for exploring and investigating high-performance electronic advanced devices under extreme conditions.