Room temperature angle-dispersive x-ray diffraction measurements on zircon-type EuVO4, LuVO4, and ScVO4 were performed up to 27 GPa. In the three compounds we found evidence of a pressure-induced structural phase transformation from zircon to a scheelite-type structure. The onset of the transition is near 8 GPa, but the transition is sluggish and the low- and high-pressure phases coexist in a pressure range of about 10 GPa. In EuVO4 and LuVO4 a second transition to a M-fergusonite-type phase was found near 21 GPa. The equations of state for the zircon and scheelite phases are also determined. Among the three studied compounds, we found that ScVO4 is less compressible than EuVO4 and LuVO4, being the most incompressible orthovanadate studied to date. The sequence of structural transitions and compressibilities are discussed in comparison with other zircon-type oxides.