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In pursue of a systematic characterization of rare-earth vanadates under compression, in this work we present a multifaceted study of the phase behavior of zircon-type orthovanadate PrVO$_4$ under high pressure conditions, up until 24 GPa. We have found that PrVO$_4$ undergoes a zircon to monazite transition at around 6 GPa, confirming previous results found by Raman experiments. A second transition takes place above 14 GPa, to a BaWO$_4$-I--type structure. The zircon to monazite structural sequence is an irreversible first-order transition, accompanied by a volume collapse of about 9.6%. Monazite phase is thus a metastable polymorph of PrVO$_4$. The monazite-BaWO$_4$-II transition is found to be reversible instead and occurs with a similar volume change. Here we report and discuss the axial and bulk compressibility of all phases. We also compare our results with those for other rare-earth orthovanadates. Finally, by means of optical-absorption experiments and resistivity measurements we determined the effect of pressure on the electronic properties of PrVO$_4$. We found that the zircon-monazite transition produces a collapse of the band gap and an abrupt decrease of the resistivity. The physical reasons for this behavior are discussed. Density-functional-theory simulations support our conclusions.