A general strategy was developed for the synthesis of new fully decorated 1,2,3‐triazoles (4a–4m and 5a–5g) containing quinazolines from 1‐(4‐nitrophenyl)‐2‐(quinazolin‐8‐ylsulfonyl) ethan‐1‐one and several azides using Ramachary organocatalytic azide‐ketone cycloaddition method. This reaction is reported for the synthesis of fully substituted sulfonyl‐1,2,3‐triazolyl quinazolins at a temperature of 100°C and the yields of the products produced are satisfactory to excellent. In vitro anticancer activity of all these derivatives demonstrated that six compounds, 4d, 4f, 4i, 4j, 5d, and 5e, were effective against two human breast cancer cell lines, MCF‐7 and MDA‐MB‐231. Compounds 4f, 4j, and 5d had more action against both cell lines than Erlotinib. Later, the findings of inhibitory assays of potent compounds 4d, 4f, 4i, 4j, 5d, and 5e against the tyrosine kinase EGFR revealed that compound 5d proved more potent than the reference erlotinib, while 4f and 4j had comparable efficacy. In silico molecular docking studies were also performed on six strong medicines to identify interactions with the EGFR receptor, and the energy estimations were shown to be comparable with the observed IC50 values. Ultimately, using SWISS/ADME and pkCSM, the in silico pharmacokinetic profile of potent compounds 4d, 4f, 4i, 4j, 5d, and 5e was predicted. All of the compounds precisely followed the principles established by Lipinski, Veber, Egan, and Muegge.