A green “polyol method” is reported for the synthesis of Cu₂O nanoparticles (NPs) immobilized on graphene oxide (Cu₂O-GO), for the first time. The composition of the synthesised composite was characterized by FT-IR, Raman, PXRD, FESEM, high-resolution TEM, XPS, TGA and ICP-MS analysis. Its catalytic application, as a novel heterogeneous catalyst, has been investigated in the solvent-free synthesis of a series of pharmaceutically important heterocycles containing nitrogen, viz. 1,2,4-triazoles and imidazo[1,2-a]pyridines. The composite shows an extensive substrate scope and broad functional group resilience. This green methodology involves the use of inexpensive reactants, moderate temperature, and solvent-free conditions and affords an excellent yield of products. The composite is retrieved from reaction mixtures by filtration and can be reused up to five cycles without any noticeable loss in its catalytic activity for both reactions.