The present work demonstrates a low-cost, single-step route for synthesizing ZnO, CuO, and ZnO–CuO nanomaterials using oxalic acid as a precipitating agent, avoiding using other surfactants. The current research also demonstrates the chemical reduction method for incorporating Ag nanoparticles onto the surface of the synthesized metal oxide nanostructures using sodium borohydride as the reductant. X-ray diffraction studies reveal the phase purity and crystallinity of the nanoparticles, while X-ray Photoelectron Spectroscopy characterizes the chemical states of surface elements. UV–vis spectra of the samples disclose the modifications shaped by Ag nanoparticles in the absorption characteristics and energy band gap of ZnO, CuO, and ZnO–CuO nanomaterials. The catalytic potentials of the synthesized materials are tested by monitoring degradation reactions of hazardous organic pollutants, including methylene blue and methyl orange, within a few minutes. The significant finding of the present study emphasizes the incorporation of Ag nanoparticles to ZnO–CuO nanocomposite and the use of sodium borohydride in photocatalysis effectively to enhance the rates of degradation of pollutant dyes without the use of intense radiation or unique lamps by initiating a three-stage electron transfer mechanism.