A new set of penta-coordinated copper(II) hydrazone complexes containing solvated methanol were synthesized by reacting the hydrazone ligands, 2-acetylpyridine benzoyl hydrazone (HL1) and 2-acetylpyridine thiophene-2-carboxylic acid hydrazone (HL2), with [CuCl2(DMSO)2] and characterized by different spectral methods. Single crystal X-ray diffraction studies of the complexes revealed that both of them, [CuCl(L1)(MeOH)] (1) and [CuCl(L2)(MeOH)] (2), have square pyramidal geometry around the cupric ion, in which the hydrazone is coordinated through NNO atoms along with a molecule of methanol in the apical position. Interaction of the ligands HL1 and HL2 along with the corresponding copper complexes 1 and 2 with calf thymus DNA (CT-DNA) has been estimated by absorption and emission titration methods which revealed that the compounds interacted with CT-DNA through intercalation. Binding of the compounds, i.e., free ligands and complexes (1) and (2) with bovine serum albumin (BSA) protein investigated using UV-visible, fluorescence and synchronous fluorescence spectroscopic methods indicated that there occurred strong binding of copper complexes to BSA over the ligands. Further, the cytotoxicity of the compounds examined in vitro on a panel of cancerous cell lines such as a human cervical cancer cell line (HeLa), a pancreatic cancer cell line (PANC-1), an Ehrlich ascites cancer cell line (EAC) and Dalton's lymphoma ascitic cancer cells (DLA) and a normal mouse embryonic fibroblasts cell line (NIH3) demonstrated that the complexes 1 and 2 possessed superior cytotoxicity than that of well-known commercial anticancer drug cisplatin to the tumor cells but are less toxic to the normal cell line and have emerged as potential candidates for further studies.