Following recent experiments [Science 2010, 328, 1543; PNAS 2011, 108, 965], we report an ab initio nonadiabatic molecular dynamics (NAMD) simulation of the ultrafast photoinduced electron transfer (ET) from a PbSe quantum dot (QD) into the rutile TiO2 (110) surface. The system forms the basis for QD-sensitized semiconductor solar cells and demonstrates that ultrafast interfacial ET is instrumental for achieving high efficiencies in solar-to-electrical energy conversion. The simulation supports the observation that the ET successfully competes with energy losses due to electron-phonon relaxation. The ET proceeds by the adiabatic mechanism because of strong donor-acceptor coupling. High frequency polar vibrations of both QD and TiO2 promote the ET, since these modes can rapidly influence the donor-acceptor state energies and coupling. Low frequency vibrations generate a distribution of initial conditions for ET, which shows a broad variety of scenarios at the single-molecule level. Compared to the molecule-TiO2 interfaces, the QD-TiO2 system exhibits pronounced differences that arise due to the larger size and higher rigidity of QDs relative to molecules. Both donor and acceptor states are more delocalized in the QD system, and the ET is promoted by optical phonons, which have relatively low frequencies in the QD materials composed of heavy elements. In contrast, in molecular systems, optical phonons are not thermally accessible under ambient conditions. Meanwhile, TiO2 acceptor states resemble surface impurities due to the local influence of molecular chromophores. At the same time, the photoinduced ET at both QD-TiO2 and molecule-TiO2 interfaces is ultrafast and occurs by the adiabatic mechanism, as a result of strong donor-acceptor coupling. The reported state-of-the-art simulation generates a detailed time-domain atomistic description of the interfacial ET process that is fundamental to a wide variety of applications.