The two major UV-induced DNA lesions, the cyclobutane pyrimidine dimers (CPD) and (6-4) pyrimidine-pyrimidone photoproducts, can be repaired by the light-activated enzymes CPD and (6-4) photolyases, respectively. It is a long-standing question how the two classes of photolyases with alike molecular structure are capable of reversing the two chemically different DNA photoproducts. In both photolyases the repair reaction is initiated by photoinduced electron transfer from the hydroquinone-anion part of the flavin adenine dinucleotide (FADH(-)) cofactor to the photoproduct. Here, the state-of-the-art XMCQDPT2-CASSCF approach was employed to compute the excitation spectra of the respective active site models. It is found that protonation of His365 in the presence of the hydroquinone-anion electron donor causes spontaneous, as opposed to photoinduced, coupled proton and electron transfer to the (6-4) photoproduct. The resulting neutralized biradical, containing the neutral semiquinone and the N3'-protonated (6-4) photoproduct neutral radical, corresponds to the lowest energy electronic ground-state minimum. The high electron affinity of the N3'-protonated (6-4) photoproduct underlines this finding. Thus, it is anticipated that the (6-4) photoproduct repair is assisted by His365 in its neutral form, which is in contrast to the repair mechanisms proposed in the literature. The repair via hydroxyl group transfer assisted by neutral His365 is considered. The repair involves the 5'base radical anion of the (6-4) photoproduct which in terms of electronic structure is similar to the CPD radical anion. A unified model of the CPD and (6-4) photoproduct repair is proposed.