The stability, electronic, and transfer properties of a photo-sensitizer donor-(pi-bridge)-acceptor (D-pi-A) zincporphyrin dye adsorbed on anatase TiO2(101) and TiO2(001) surfaces are studied by periodic density functional theory calculations, including the screened hybrid functional. We also study the dye adsorption on the TiO2(101) surface with an oxygen vacancy. Our results show that the deprotonated dye attaches strongly on surface Ti-5c atoms forming both bidentate bridging and chelating linkage modes. The protonated dye is found stable on pristine TiO2(101), forming the monodentate linkage mode. However, on TiO2(001) and defective TiO2(101), the monodentate mode stabilizes after a spontaneous dye deprotonation. The electronic band structure of the TiO2-dye assemblies shows the dye lowest-unoccupied molecular-orbital resonant with TiO2 conduction bands, exhibiting a strong hybridization, where the electron injection potentials are calculated around 1 eV for all systems under study. This high value, together with the favorable electronic coupling, suggest a fast electron injection from the dye into the semiconductor as experimentally reported. Moreover, the electronic properties of TiO2-dye assemblies show similarities independent of the adsorption modes or the surface characteristic, suggesting that the high efficiency of anatase TiO2-based dye sensitized solar cell resides largely in its favorable electron injection properties.