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We report the first observation of a pressure-induced transition from a superconducting (SC) to an insulating (I) phase in single-crystal Ba1-xKxBiO3 (x = 0.4, 0.43, 0.52, and 0.58) superconductors. X-ray diffraction measurements conducted at 20 K reveal a direct relationship between this SC-I transition and a pressure-induced distortion of crystal structure. With increasing pressure, the lattice parameters a and c of the ambient-pressure superconducting tetragonal (T) phase are compressed continuously below a critical pressure (Pc1), wherein the pressure (P) dependence of superconducting transition temperature (Tc) displays a small variation. However, upon further compression, the lattice of the compressed T phase displays an anisotropic change, and Tc shows a monotonous decrease. When the pressure reaches Pc2 (Pc2 > Pc1), the compressed T phase collapses along the c axis, followed by the disappearance of superconductivity and the appearance of the insulating phase. This SC-I transition is fully reversible, with the critical pressure increasing alongside K doping concentration. These findings are strikingly similar to the SC-I transition observed in hole-doped high-Tc cuprate superconductors under pressure. Identifying their commonalities could deepen our understanding of the mechanisms that underlie high- Tc superconductivity in these two oxide superconductors with a perovskite structure.