An unprecedented oxidative cyclodimerization reaction of 2H-azirine-2-carboxylates to pyrimidine-4,6-dicarboxylates under heating with triethylamine in air is described. In this reaction, one azirine molecule undergoes formal cleavage across the C-C bond and another across the C=N bond. According to the experimental study and DFT calculations, the key steps of the reaction mechanism include nucleophilic addition of N,N-diethylhydroxylamine to an azirine to form an (aminooxy)aziridine, generation of an azomethine ylide, and its 1,3-dipolar cycloaddition to the second azirine molecule. The crucial condition for the synthesis of pyrimidines is generation of N,N-diethylhydroxylamine in the reaction mixture in a very low concentration, which is ensured by the slow oxidation of triethylamine with air oxygen. Addition of a radical initiator accelerated the reaction and resulted in higher yields of the pyrimidines. Under these conditions, the scope of the pyrimidine formation was elucidated, and a series of pyrimidines was synthesized.