Topoisomerase (IIB) inhibitors have been involved in the therapies of tumour progression and have become a major focus for the development of anticancer agents. New three-component hybridised ligands, 1,4-disubstituted-1,2,3-triazoles (8–17), were synthesised via a 1,3-dipolar cycloaddition reaction of 9-azidoacridine/3-azidocoumarin with N/O-propargyl small molecules under click reaction conditions. Cancer cell growth inhibition of the synthesised triazoles was tested against human cell-lines in the NCI-60-cell-panel, and the most active compounds tested against topoisomerase (IIB)-enzymes. The acridinyl ligands (8–10) revealed 60–97% cell growth inhibition in six cancer cell-panels. Cell-cycle analysis of MCF7 and DU-145 cells treated with the active acridinyl ligands exhibited cell-cycle arrest at G2/M phase and proapoptotic activity. In addition, compound 8 displayed greater inhibitory activity against topoisomerase (IIB) (IC₅₀ 0.52 µM) compared with doxorubicin (IC₅₀ 0.83 µM). Molecular dynamics simulation studies showed the acridine–triazole–pyrimidine hybrid pharmacophore was optimal with respect to protein–ligand interaction and fit within the binding site, with optimal orientation to allow for intercalation with the DNA bases (DG13, DC14, and DT9).