This paper reports the synthesis and detailed characterisation of copper(II) and nickel(II) complexes with tridentate thiosemicarbazone ligands H2L1 and H2L2 derived from 2-acetylpyrazine. The ligands and their metal complexes were characterised by different physicochemical techniques, including elemental and thermogravimetric analysis; UV-Vis, IR, 1H-NMR, and 13C-NMR spectroscopy; molar conductance measurements; and mass spectrometry. The crystal structure of the H2L1 ligand was determined by single crystal X-ray diffraction studies. The spectral data showed that the thiosemicarbazone behaves as an NNS tridentate ligand through the nitrogen atoms of the azomethine group and pyrazine ring and the sulphur atom of the thioamide group. Elemental and thermal analyses indicated that the obtained metal complexes had a 1 : 1 stoichiometry (metal-ligand). The interactions between these complexes and calf thymus DNA (CT-DNA) were studied by electronic absorption and viscosity measurements. The activities of these compounds against oxidative DNA cleavage were examined by agarose gel electrophoresis. Cu(II) and Ni(II) complexes can wind DNA strands through groove interactions and promote strand breakage of the plasmid pmCherry under oxidative stress conditions. Moreover, all the complexes could interact more strongly with DNA than could with the free ligands. Finally, the antibacterial activities of the ligands and their complexes were determined by in vitro tests against Gram-positive bacterial strains (S. aureus ATCC 25923, L. monocytogenes ATCC 19115, and B. cereus ATCC 10876) and Gram-negative bacterial strains (E. coli ATCC 25922, S. typhimurium ATCC 14028, and K. pneumoniae ATCC BAA-2146) using the broth microdilution method. The metal complexes showed greater antimicrobial activities than the precursor ligands against some of the microorganisms.