BaVS3 presents a metal-to-insulator (MI) transition at ambient pressure due to the stabilization of a 2k(F) commensurate charge density wave (CDW) Peierls ground state built on the dz(2) V orbitals. The MI transition vanishes under pressure at a quantum critical point (QCP) where the electronic properties exhibit a non-Fermi liquid behavior. In this paper, we determine the CDW phase diagram under pressure and show that it combines both the vanishing of the second-order Peierls transition and a commensurate-incommensurate first-order delocking transition of the 2k(F) wave vector. We explain quantitatively the drop of the MI critical temperature by the decrease of the electron-hole pair lifetime of the CDW condensate due to an enhancement of the hybridization between the dz(2) and e(t(2g)) levels of the V under pressure.