A series of novel 1,4-naphthoquinone–triazole hybrids, N-(3-amino-1,4-dioxo-1,4-dihydronaphthalen-2-yl)-2-(4-R-1H-1,2,3-triazol-1-yl)acetamide, was synthesized by click chemistry in the presence of sodium ascorbate and copper(II) sulfate pentahydrate in 81–94% yield. Various biological properties of the synthesized compounds including DNA binding/cleavage, antioxidant, antibacterial and antifungal properties were evaluated. The DNA binding study was performed using dsDNA and G-quadruplex DNA. All of the compounds showed fluorescence increase in the presence of DNA, regardless of the structure. Up to 2.9 and 2.5 times fluorescence increase upon incubation with double stranded or G-quadruplex DNA was detected for 5f and 5g, respectively. The docking studies performed on dsDNA and G-quadruplex structures suggested compounds’ mode of interactions were populated around the grooves. All of the compounds showed excellent DNA cleavage activity and 5e was almost degraded the plasmid DNA. The highest radical scavenging activity was obtained as 89.9% at 200 mg/L with 5d. However, the highest ferrous chelating activity was obtained as 68.1% at 200 mg/L with 5g. The compounds exhibited antimicrobial activity against Bacillus cereus, Legionella pneumophila subsp. pneumophila, Staphylococcus aureus, Pseudomonas aeruginosa, Escherichia coli and Enterococcus hirae as bacteria strains and Candida albicans and Candida tropicalis as microfungus strains. The compounds exhibited antibacterial and antifungal activity in the range of 4–128 μg/mL and 16–128 μg/mL, respectively. The best antimicrobial activity was obtained with 5d and 5e with a MIC value of 4 μg/mL against Enterococcus hirae. The acid dissociation constants (pKa) were determined potentiometrically in 20% (v/v) dimethyl sulfoxide-water hydro-organic solvent at an ionic background of 0.1 mol/L of NaCl, at 25 ± 0.1 °C. Five pKa values were obtained for each ligand.