The compounds 2a-2h containing a thiazolidinone pharmacophore were synthesized via hetrerocylization of thiosemicarbazones with dimethyl acetylenedicarboxylate. The hybrid molecules were evaluated for anticancer activity against the human cell lines MCF-7, T47D (human breast adenocarcinoma) and HeLa (cervical cancer). Compounds 2c showed effective cytotoxicity on MCF-7 and HeLa (GI50 6.40 ± 0.10 μM/mL and GI5010.30 ± 1.09 μM/mL), and compound 2d also showed effective cytotoxicity against MCF-7 and HeLa cell lines i.e., (GI50 16.60 ± 0.21 μM/mL and GI50 15.02 ± 0.14 μM/mL). These findings were comparable to cisplatin (azane;dichloroplatinum) the standard drug (GI50 13.20 ± μM/mL and 15.10 μM/mL respectively) and consequently nominated for determination of the mode of cell death. The results revealed the cytotoxic effects of 2c and 2d by induction of apoptosis in MCF-7 and HeLa cell lines. Moreover the results were further supported by the Molecular Docking which predicts the binding interactions of the best anticancer ligands with Ribonucleotide reductase (RNR), which is essential enzyme required for de-novo synthesis of DNA precursors. Molecular dynamic simulations were also performed to determine the stability of protein-ligand complex under different simulated conditions. In addition, the computational studies including DFTs, ADMET properties suggested these compounds can act as lead molecules, for the synthesis of novel drug candidates for the treatment of specific cancer and its associated malignancies.