Two-phase transport with simultaneous component adsorption and mechanical entrapment occurs in numerous suspension and nano-colloidal flows in porous media, including polymer flooding in oilfields. To the contrary of one-dimensional (1D) self-similar solution for polymer flooding that ignores the mechanical entrapment, accounting for this phenomenon breaks self-similarity. However, this non-self-similar problem allows for an exact integration. For the first time, the present work derives an exact solution for polymer injection into a rock saturated by oil and water with simultaneous adsorption and mechanical entrapment. The splitting method that uses Lagrangian coordinate as an independent variable instead of time, splits the 3 x 3 governing system into 2 x 2 auxiliary system that determines suspended and captured polymer concentrations, and the scalar equation for unknown phase saturation. The exact solution reveals two fingerprints of the component entrapment under small entrapped concentrations: stabilisation of the breakthrough concentration at the value below the injected one, and non-stabilised pressure drop growth. Three sets of laboratory polymer core-floodings exhibit a close match by the analytical model.