Combined analyses of experimental and computational studies on the Cu-catalyzed three-component reactions of sulfonyl azides, terminal alkynes and amines, alcohols, or water are described. A range of experimental data including product distribution ratio and trapping of key intermediates support the validity of a common pathway in the reaction of 1-alkynes and two distinct types of azides substituted with sulfonyl and aryl(alkyl) groups. The proposal that bimolecular cycloaddition reactions take place initially between triple bonds and sulfonyl azides to give N-sulfonyl triazolyl copper intermediates was verified by a trapping experiment. The main reason for the different outcome from reactions between sulfonyl and aryl(alkyl) azides is attributed to the lability of the N-sulfonyl triazolyl copper intermediates. These species are readily rearranged to another key intermediate, ketenimine, into which various nucleophiles such as amines, alcohols, or water add to afford the three-component coupled products: amidines, imidates, or amides, respectively. In addition, the proposed mechanistic framework is in good agreement with the obtained kinetics and competition studies. A computational study (B3LYP/LACV3P*+) was also performed confirming the proposed mechanistic pathway that the triazolyl copper intermediate plays as a branching point to dictate the product distribution.