A single polymer flooding is a widely employed enhanced oil recovery method, despite polymer vulnerability to shear and thermal degradation. Nanohybrids, on the other hand, resist degradation and maintain superior rheological properties at different shear rates. In this article, the effect of coupling CuO nanoparticles (NPs) and nanoclay with partially hydrolyzed polyacrylamide (HPAM) polymer solution on the rheological properties and the recovery factor of the nanohybrid fluid was assessed. The results confirmed that the NP agents preserved the polymer chains from degradation under mechanical, chemical (i.e., salinity), and thermal stresses and maintained good extent of entanglement among the polymer chains, leading to a strong viscoelastic attribute, in addition to the pseudoplastic behavior. The NP additives increased the viscosity of the HPAM polymer at shear rates varying from 10−100 s−1. The rheological properties of the nanohybrid systems varied with the NP additive content, which in turn provided a window for engineering a nanohybrid system with a proper mobility ratio and scaling coefficient, while avoiding injectivity issues. Sandpack flooding tests confirmed the superior performance of the optimized nanohybrid system and showed a 39% improvement in the recovery ratio relative to the HPAM polymer injection.