We herein report the design and synthesis of new 1,3,5-triazine-based pyrazole derivatives (5a–i) with anticancer activity targeting the epidermal growth factor (EGFR) tyrosine kinase. The newly synthesized compounds were characterized using spectroscopic techniques such as ¹H NMR, ¹³C NMR, mass spectrometry and elemental analysis. All the compounds exhibited moderate to good anticancer activity against MCF-7 (human breast), HepG2 (human liver), HCT116 (human colorectal), PC-3 (human prostate), LoVo (human colon) and LoVo/DX (doxorubicin-resistant) cancer cell lines except compound 5i, which exhibited poor activity. Compounds 5f, 5g and 5h possessed more promising anticancer activity and the results were expressed as IC₅₀ values in nM. These compounds also displayed potent inhibitory activity against EGFR-tyrosine kinase with IC₅₀ values of 395.1, 286.9 and 229.4 nM, respectively in comparison with the standard drug, erlotinib. The docking studies revealed that the compounds showed a good affinity towards the target EGFR kinase (PDB ID: 6V6O) by forming multiple H-bonds with amino acids. The binding interaction of the more active compounds (5f, 5g and 5h) with Ct-DNA was explored using spectroscopic, viscometric, electrochemical and docking techniques. Both the experimental and theoretical findings of DNA binding showed consistent results and confirmed the groove mode of interaction of these compounds with DNA. The in vitro ADME properties were also evaluated, thus allowing the identification of optimized compounds as promising anticancer agents. Finally, density functional theory (DFT) geometry optimization and the relevant quantum parameters were calculated for the active compounds using the B3LYP level.