Rhodium(II) azavinyl carbenes, conveniently generated from 1-sulfonyl-1,2,3-triazoles, undergo a facile, mild and convergent formal 1,3-insertion into N–H and O–H bonds of primary and secondary amides, various alcohols, and carboxylic acids to afford a wide range of vicinally bis-functionalized Z-olefins with perfect regio- and stereoselectively. Utilizing the distinctive functionality installed through these reactions, a number of subsequent rearrangements and cyclizations expand the repertoire of valuable organic building blocks constructed by reactions of transition metal carbene complexes, including α-allenyl ketones and amino-substituted heterocycles.