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Three nitro-substituted 2,3-dihydro-1H-perimidine derivatives (ortho, meta-, and para-nitrophenyl) were synthesised via a novel, additive-free ultrasonication-assisted method with high yields (up to 90%). Their structures were validated experimentally and supported by DFT calculations, which also provided insight into the reaction mechanism. Further molecular docking, integrated with MD simulation studies, against the identified EGFR mutants revealed strong binding affinities and stable interactions, especially for the ortho-nitro derivative. To validate these findings, we performed ADME and toxicity analyses that confirmed favourable drug-likeness and safety profiles. Potent anticancer activity consistent with computational predictions was confirmed by MTT assays on NCI-H460 cells. Cell cycle analysis showed that the compounds induced phase-specific arrest, contributing to reduced cell viability. Apoptosis was further validated by Annexin V flow cytometry and AO/EB fluorescence imaging, which revealed early and late apoptotic populations. Overall, the compounds demonstrated strong apoptotic and antiproliferative activity.