CdTe/ZnSe core/shell quantum dot (QD), one of the strongest and most highly luminescent nanoparticles, was directly synthesized in an aqueous medium to study its individual interactions with important nucleobases (adenine, guanine, cytosine, and thymine) in detail. The results obtained from the optical analyses indicated that the interactions of the QDs with different nucleobases were different, which reflected in different fluorescent emission maxima and intensities. The difference in the interaction was found due to the different chemical behavior and different sizes of the formed nanoconjugates. An electrochemical study also confirmed that the purines and pyrimidines show different interactions with the core/shell QDs. Based on these phenomena, a novel QD-based method is developed to detect the presence of the DNA, damage to DNA, and mutation. The QDs were successfully applied very easily to detect any change in the sequence (mutation) of DNA. The QDs also showed their ability to detect DNAs directly from the extracts of human cancer (PC3) and normal (PNT1A) cells (detection limit of 500 pM of DNA), which indicates the possibilities to use this easy assay technique to confirm the presence of living organisms in extreme environments.