We performed high-pressure x-ray diffraction (XRD), Raman, and transport measurements combined with first-principles calculations to investigate the behavior of tin diselenide (SnSe2) under compression. The obtained single-crystal XRD data indicate the formation of a (1/3,1/3,0)-type superlattice above 17 GPa. According to our density functional theory results, the pressure-induced transition to the commensurate periodic lattice distortion (PLD) phase is due to the combined effect of strong Fermi surface nesting and electron-phonon coupling at a momentum wave vector q=(1/3,1/3,0). In contrast, similar PLD transitions associated with charge density wave (CDW) orderings in transition metal dichalcogenides (TMDs) do not involve significant Fermi surface nesting. The discovered pressure-induced PLD is quite remarkable, as pressure usually suppresses CDW phases in related materials. Our findings, therefore, provide new playgrounds to study the intricate mechanisms governing the emergence of PLD in TMD-related materials.