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 bisfunctionalized (Z)-olefins with perfect regio- and stereo-selectivity. 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 a-allenyl ketones and amino-substituted heterocycles.