Plasmon resonances in metal nanoparticles (MNPs) can be used to enhance the efficiency of photoinduced electron transfer from a sensitizer (a molecule or a quantum dot (QD)) to a semiconductor electrode. Here we use a model Hamiltonian approach to study the optical response and the steady state electron injection rate (SSIR) of a hybrid system, consisting of a sensitizer that is coupled to a metal nanoparticle via dipole coupling and to a semiconductor electrode via electronic coupling. Counterintuitively, the total absorption cross section for the coupled system and the SSIR are correlated only for small coupling; in the relevant domain of large enhancement we observe anticorrelation. A maximum SSIR as a function of the dipole coupling strength is predicted analytically, and shown to result from the competition between the plasmonic field enhancement and the Purcell effect. In the case of pulsed excitation, the appearance of a Fano resonance and its reversal is illustrated as the dipole coupling strength grows, and for strong couplings Rabi splitting is observed. Interestingly, in the case of continuous wave (CW) excitation, we find plasmon-induced resonance energy transfer, leading to strong SSIR at incident light frequencies that are far detuned from the sensitizer transition frequency and are fully controllable.