The reaction of singlet molecular oxygen with purine DNA bases is investigated by computational means. We support the formation of a transient endoperoxide for guanine and by classical molecular dynamics simulations we demonstrate that the formation of this adduct does not affect the B-helicity. We thus identify the guanine endoperoxide as a key intermediate, confirming a low-temperature nuclear magnetic resonance proof of its existence, and we delineate its degradation pathway, tracing back the preferential formation of 8-oxoguanine versus spiro-derivates in B-DNA. Finally, the latter oxidized 8-oxodGuo product exhibits an almost barrierless reaction profile, and hence is found, coherently with experience, to be much more reactive than guanine itself. On the contrary, in agreement with experimental observations, singlet-oxygen reactivity onto adenine is kinetically blocked by a higher energy transition state.