Photoinduced electron-transfer processes in the dye-semiconductor system alizarin-TiO₂ are studied. The study is based on a recently developed method, which uses first-principles electronic structure calculations to characterize the system and to parametrize a model Hamiltonian including electronic-vibrational coupling. On the basis of this modeling procedure, accurate quantum dynamical simulations are performed, employing the multilayer multiconfigurational time-dependent Hartree method. The results of the simulations show that the electron injection process in this system takes place on an ultrafast femtosecond time scale and is accompanied by significant electronic coherence effects. A detailed analysis reveals that the electron-transfer process proceeds via a two-step mechanism involving an intermediate state localized at the dye-substrate interface.