In the pursuit 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 PrVO4 under high-pressure conditions, up to 24 GPa. We have found that PrVO4 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 BaWO4-II type structure. The zircon to monazite structural sequence is an irreversible first-order transition, accompanied by a volume collapse of about 9.6%. The monazite phase is thus a metastable polymorph of PrVO4. The monazite-BaWO4-II transition is found instead to be reversible 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 PrVO4. We found that the zircon-monazite transition produces a collapse of the band gap and an abrupt decrease in the resistivity. The physical reasons for this behavior are discussed. Density functional theory simulations support our conclusions.