Synchrotron X-ray diffraction measurements on lead sulfate have been performed up to 67 GPa using He as pressure transmitting medium. Experiments reveal the existence of a reversible pressure-induced phase transition from the initial Pnma barite-type to the P212121 post-barite-type structure at pressures above 27 GPa. This phase transition involves a volume collapse of 2.4% and requires a considerable pressure overshoot (large pressure range with coexistence of phases) to overcome the large kinetic barrier of the transition. DFT calculations confirm the experimental observations and support the hypothesis that post-barite-type phase is the thermodynamically stable high-pressure structure for ABO4 ternary oxides with large A and small B atoms. The mechanism of the phase transition is described, and the compressibility and anisotropy of both polymorphs are estimated.