A supported catalyst has been prepared by immobilization of a copper(II) complex of 4′-phenyl-2,2′:6′,2′′-terpyridine on activated multiwalled carbon nanotubes [AMWCNTs-O-CuII-PhTPY]. This heterogeneous catalyst was characterized by scanning electron microscopy (SEM), transmission electron microscopy (TEM), atomic force microscopy (AFM), inductively coupled plasma (ICP) analysis, UV/vis and FT-IR techniques. To ensure the efficiency and fidelity of the copper species, the implementation of three-component strategies in click chemistry was tested. The catalyst enabled the development of one-pot, two-step, mild, and environmentally benign syntheses of diversely decorated 1,2,3-triazoles from alkynes, epoxides or benzyl/alkyl halides, and sodium azide in water. The complex has high catalytic activity, regioselectivity, and was recycled five successive times. In another experiment, the vasorelaxing effect of the triazole products was studied in isolated rat thoracic aorta. All of the selected compounds are vasorelaxants, based on the IC50 values obtained, and the vasorelaxing potency and maximal response for three of the compounds are comparable to acetylcholine.