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We present a comprehensive study of the inhomogeneous mixed-valence compound, EuPd₃S₄, by electrical transport, X-ray diffraction, time-domain¹⁵¹Eu synchrotron Mössbauer spectroscopy, and X-ray absorption spectroscopy measurements under high pressure. Electrical transport measurements show that the antiferromagnetic ordering temperature,T_N, increases rapidly from 2.8 K at ambient pressure to 23.5 K at ~19 GPa and plateaus between ~19 and ~29 GPa after which no anomaly associated withT_Nis detected. A pressure-induced first-order structural transition from cubic to tetragonal is observed, with a rather broad coexistence region (~20 GPa to ~30 GPa) that corresponds to theT_Nplateau. Mössbauer spectroscopy measurements show a clear valence transition from approximately 50:50 Eu²⁺:Eu³⁺to fully Eu³⁺at ~28 GPa, consistent with the vanishing of the magnetic order at the same pressure. X-ray absorption data show a transition to a fully trivalent state at a similar pressure. Our results show that pressure first greatly enhancesT_N, most likely via enhanced hybridization between the Eu 4fstates and the conduction band, and then, second, causes a structural phase transition that coincides with the conversion of the europium to a fully trivalent state.