One-pot synthesis of colloidal Au/ZnO and Ag/ZnO nanohybrid structures was carried out. The copolymers of maleic acid—poly(N-vinyl-2-pyrrolidone-alt-maleic acid), poly(ethylene-alt-maleic acid), or poly(styrene-alt-maleic acid) were used as templates for the sorption of cations of metals-precursors and stabilization of the resulting nanoheterostructures. Simultaneous production of two types of nanoparticles has been implemented under mild conditions in an aqueous alkaline medium and without additional reagents. Equimolar ratios of the metal cations and appropriate load on all copolymers were used: molar ratio of maleic acid monomeric units of copolymer/gold (silver)cations/zinc cations was 1/0.15/0.23 (1/0.3/0.15). The process of obtaining the heterostructures was studied using UV-Vis spectroscopy. The kinetics of the formation of heterostructures was influenced by the nature of the maleic acid copolymer and noble metal cations used. A high reaction rate was observed in the case of using zinc and gold cations-precursors and a copolymer of maleic acid with N-vinylpyrrolidone as a stabilizer of nanoparticles. The structure of the synthesized polymer-stabilized heterostructures was studied using instrumental methods of analysis—XPS, FTIR, PXRD, and TEM. Under the conditions used, stable colloidal solutions of heterodimers were obtained, and such structure can be converted to a solid state and back without loss of properties.