The boundary layer fluid flow past a wedge surface occurs in various industrial processes, including wire drawing, metal foaming, polymer extraction, fiber processing, and in determining the dynamic properties (shear stress, drag) of working fluids. Theoretically, the boundary layer three-dimensional flow of a magnetized hybrid nanoliquid over a wedge surface is studied with viscous dissipation and radiation effects. The flow is due to moving wedge surface and power-law free-stream velocities. The current study unifies three different classical flow problems, namely, the Blasius flow, the Hiemenz flow, and the Falkner-Skan flow. Single-phase description of hybrid nanofluid is considered, and the problem is kept realistic by considering the experimental thermophysical properties of the nanomaterial. The governing system consists of conservation of mass, momentum, and the energy equations for hybrid nanofluids. Prandtl’s boundary layer approximations are applied to study the viscous dominant fluid regimes. The entropy equation and the Bejan number are also derived. Numerical computations of self-similar equations are obtained to explore the rheological and the heat transport features against the physical parameters. The Nusselt number and the drag on the wedge surface are computed and analyzed. Of the three classical flow problems, the maximum thickness of the momentum layer occurs for the Blasius flow problem. A minimum drag force on the wedge surface occurs for lower Hartmann number values. Furthermore, an increase in the volume fraction of the hybrid nanoparticles leads to an enhanced heat transport. The use of carbon nanotubes which has exceptional characteristics are taken into consideration in this study. This study also demonstrates the comparison on three-different classical flow problems (Blasius flow, Hiemenz flow, and Falkner-Skan flow).