A simple method involving microwave-assisted reaction of 3-benzylthiazolium/benzothiazolium bromides with cuprous oxide has been developed for the synthesis of four new N-heterocyclic carbene (NHC): thiazolylidene/benzothiazolylidene–Cu(I) complexes. Structures of the complexes could be established on the basis of the IR, 1H, and 13C NMR studies and elemental analysis. A representative NHC:benzothiazolylidene–Cu(I) complex was used as catalyst for the microwave-assisted A3 reaction of phenylacetylene with a secondary amine and aldehyde to obtain new substituted propargylamines in excellent yields. A theoretical investigation of the model A3 reaction at the DFT level reveals initial coordination of the alkyne with the NHC–Cu(I) complex followed by its attack on the iminium ion generated from the reaction of secondary amine with aldehyde. In the presence of the catalyst, the activation free energy barrier (ΔG#) is lowered by ca. 3 kcal mol−1.