A new series of compounds planned by molecular hybridization of the nucleobases uracil and thymine, or the xanthine theobromine, with coumarins, and linked through 1,2,3-triazole heterocycles were evaluated for their in vitro anticancer activity against the human tumor cell lines: colon carcinoma (HCT116), laryngeal tumor cells (Hep-2), and lung carcinoma cells (A549). The hybrid compound 7a exhibited better activity in the series, showing an IC50 of 24.19 ± 1.39 μM against the HCT116 cells, with a selectivity index (SI) of 6, when compared to the cytotoxicity against the non-tumor cell line HaCat. Molecular docking studies were performed on all active compounds and suggested that the synthesized compounds possess a high affinity to DNA Topoisomerase-1 protein, supporting their antitumor activity. The in silico toxicity prediction studies suggest that the compounds present a low risk of causing theoretical mutagenic and tumorigenic effects. These findings indicate that the molecular hybridization from natural derivative molecules is an interesting approach to seek new antitumor candidates.