Novel triazoloquinazolines carrying the 2-[thio]acetamide entity (4 and 5a–d) and triazoloquinazoline/chalcone hybrids incorporating the 2-[thio]acetamide linker (8a–b and 9a–f) were developed as anticancer candidates. NCI screening of the synthesized compounds at 10 μM concentration displayed growth inhibition not only up to 99.74% as observed for 9a but also a lethal effect could be achieved as stated for compounds 9c (RPMI-8226 and HCT-116) and 8b, 9a, and 9e on the HCT-116 cell line. The antiproliferative activity was determined for the chalcone series on three cell lines: RPMI-8226, HCT-116, and MCF-7. Compounds 8b, 9a, 9b, and 9f were the most active ones. To understand the mechanistic study, the inhibitory effect on the epidermal growth factor receptor (EGFR) kinase was evaluated. The results stated that the activity of compound 8b (IC50 = 0.07 μM) was near that of the reference drug erlotinib (IC50 = 0.052 μM) whereas compound 9b (IC50 = 0.045 μM) was found to be more potent than erlotinib. Both compounds 8b and 9b were selected for cell cycle analysis and apoptotic assays. Moreover, molecular docking results of the selected chalcone hybrids showed high binding scores and good binding affinities especially for 8b and 9b, which were consistent with the biological activity (EGFR).