A new series of benzimidazole, 1,2,4-triazole, and 1,3,5-triazine derivatives were designed and synthesized using a microwave irradiation synthetic approach utilizing 2-phenylacetyl isothiocyanate (1) as a key starting material. All the new analogues were evaluated as anticancer agents against a panel of cancer cell lines utilizing doxorubicin as a standard drug. Most of the tested derivatives exhibited selective cytotoxic activity against MCF-7 and A-549 cancer cell lines. Furthermore, the new target compounds 5, 6, and 7 as the most potent antiproliferative agents have been assessed as in vitro EGFR^WT and EGFR^T790M inhibitors compared to the reference drugs erlotinib and AZD9291. They represented more potent suppression activity against the mutated EGFR^T790M than the wild-type EGFR^WT. Moreover, the compounds 5, 6, and 7 down-regulated the oncogenic parameter p53 ubiquitination. A docking simulation of compound 6b was carried out to correlate its molecular structure with its significant EGFR inhibition potency and its possible binding interactions within the active site of EGFR^WT and the mutant EGFR^T790M.