Selective cyclooxygenase-1 (COX-1) inhibition has got into the spotlight with the discovery of COX-1 upregulation in various cancers and the cardioprotective role of COX-1 in control of thrombocyte aggregation. Yet, COX-1-selective inhibitors are poorly explored. Thus, three series of quinazoline derivatives were prepared and tested for their potential inhibitory activity toward COX-1 and COX-2. Of the prepared compounds, 11 exhibited interesting COX-1 selectivity, with 8 compounds being totally COX-1-selective. The IC value of the best quinazoline inhibitor was 64 nM. The structural features ensuring COX-1 selectivity were elucidated using in silico modeling.