A new class of pyrido[2,3-d][1,2,4]triazolo[4,3-a]pyrimidinones and pyrido[2,3-d]thiazolo[3,2-a]pyrimidinones was synthesized by reacting 5-phenyl-2-thioxo-2,3-dihydropyrido[2,3-d]pyrimidin-4(1H)-one with hydrazonoyl halides and α-bromoketones via a Knoevenagel–cyclocondensation followed by heteroannulation. Structures were confirmed by elemental analysis and IR, 1H NMR, and MS spectroscopy. Cytotoxicity against HepG2 cells (MTT assay) revealed submicromolar activity for the most active analogs (IC50 0.72–0.95 µM), comparable to doxorubicin (0.65 µM). Structure–activity trends indicate that ester functionalities, coumarin incorporation, and electron-donating aryl substituents enhance potency. Molecular docking to the EGFR kinase domain showed strong predicted binding for the top analogs (scores −9.6 to −10.2 kcal mol−1 vs −8.7 kcal mol−1 for doxorubicin), highlighting key hydrogen-bond and hydrophobic contacts with Lys745, Asp837, Arg841, and Asp855. Docking results align with the in vitro data. In silico ADMET predictions suggest favorable drug-likeness, oral absorption, and non-mutagenic character. These findings position the reported pyridopyrimidine scaffolds as promising EGFR-targeted anticancer leads.