The unclear relationship between cuprate superconductivity and the pseudogap state remains an impediment to understanding the high transition temperature (T-c) superconducting mechanism. Here, we used magnetic field-dependent scanning tunneling microscopy to provide phase-sensitive proof that d-wave superconductivity coexists with the pseudogap on the antinodal Fermi surface of an overdoped cuprate. Furthermore, by tracking the hole-doping (p) dependence of the quasi-particle interference pattern within a single bismuth-based cuprate family, we observed a Fermi surface reconstruction slightly below optimal doping, indicating a zero-field quantum phase transition in notable proximity to the maximum superconducting T-c. Surprisingly, this major reorganization of the system's underlying electronic structure has no effect on the smoothly evolving pseudogap.