The interactions with calf thymus DNA (CT-DNA) of three Schiff bases formed by the condensation of hesperetin with benzohydrazide (HHSB or L1H3), isoniazid (HIN or L2H3), or thiosemicarbazide (HTSC or L3H3) and their CuII complexes (CuHHSB, CuHIN, and CuHTSC with the general formula [CuLnH2(AcO)]) were evaluated in aqueous solution both experimentally and theoretically. UV–Vis studies indicate that the ligands and complexes exhibit hypochromism, which suggests helical ordering in the DNA helix. The intrinsic binding constants (Kb) of the Cu compounds with CT-DNA, in the range (2.3–9.2) × 106, from CuHTSC to CuHHSB, were higher than other copper-based potential drugs, suggesting that π–π stacking interaction due to the presence of the aromatic rings favors the binding. Thiazole orange (TO) assays confirmed that ligands and Cu complexes displace TO from the DNA binding site, quenching the fluorescence emission. DFT calculations allow for an assessment of the equilibrium between [Cu(LnH2)(AcO)] and [Cu(LnH2)(H2O)]+, the tautomer that binds CuII, amido (am) and not imido (im), and the coordination mode of HTSC (O−, N, S), instead of (O−, N, NH2). The docking studies indicate that the intercalative is preferred over the minor groove binding to CT-DNA with the order [Cu(L1H2am)(AcO)] > [Cu(L2H2am)(AcO)] ≈ TO ≈ L1H3 > [Cu(L3H2am)(AcO)], in line with the experimental Kb constants, obtained from the UV–Vis spectroscopy. Moreover, dockings predict that the binding strength of [Cu(L1H2am)(AcO)] is larger than [Cu(L1H2am)(H2O)]+. Overall, the results suggest that when different enantiomers, tautomers, and donor sets are possible for a metal complex, a computational approach should be recommended to predict the type and strength of binding to DNA and, in general, to macromolecules.