In the present study, a novel series of N-(6-(2,5-dimethoxypyrimidin-4-yl)pyridin-3yl)benzenesulfonamide derivatives 7(a-g) were rationally designed to block the overexpression of epidermal growth factor receptor (EGFR), a key protein involved in the progression of lung cancer. Overexpression of EGFR plays a critical role in promoting proliferation and tumor growth, making it an attractive target for the development of new anticancer agents. Initially, computer-based prediction was employed to understand the interaction of the designed molecules with the EGFR active site. The compounds were optimized and screened for their pharmacokinetic profiles, including ADMET (absorption, distribution, metabolism, excretion, and toxicity) properties. Molecular docking studies were performed using two EGFR crystal structures (PDB IDs: 1M17 and 5CAO) to predict binding affinities with the target protein. The analysis revealed promising binding scores ranging from −7.1 to −8.5 kcal/mol, indicating strong receptor binding. Notably, most designed molecules exhibited better binding scores than the clinically approved EGFR inhibitors Compound-29 and Erlotinib. Following computational evaluation, the target molecules were synthesized through two-step reactions involving sulfonamide bond formation and Suzuki–Miyaura cross-coupling, affording derivatives 7(a-g) in good yields. The synthesized compounds were characterized by IR, ¹H NMR, ¹³C NMR, and HRMS analyses. Anticancer activity was evaluated through in vitro cytotoxic studies against the human lung cancer cell line A549. Among the tested compounds, 7g displayed the most promising inhibitory activity with an IC₅₀ value of 18.04 ± 1.12 µM and EGFR inhibition with an IC₅₀ value of 7.17 ± 1.12 µM. SAR analysis indicated that the presence of the –CF₃ group and lipophilic aromatic moieties contributed to strong interactions within the active pocket, enhancing biological activity. Collectively, compound 7g emerged as the most promising candidate of the series.