We present a comprehensive study of the mixed valent compound, EuPd3S4, by electrical transport, X-ray diffraction, time-domain 151Eu synchrotron Mössbauer spectroscopy, and X-ray absorption spectroscopy measurements under high pressure. The electrical transport measurements show that the antiferromagnetic ordering temperature, TN, 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 with TN is detected. A pressure-induced first order structural transition from cubic to tetragonal is observed, with a rather broad coexistence region (~20 GPa to ~32 GPa) that corresponds to the TN plateau. 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 enhances TN, most likely via enhanced hybridization between the Eu 4f states 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.