We demonstrate a novel approach of utilizing methanol (CH3OH) in a dual role for (1) the methanolysis of polyethylene terephthalate (PET) to form dimethyl terephthalate (DMT) at near‐quantitative yields (~97%) and (2) serving as an in‐situ H2 source for the catalytic transfer hydrogenolysis (CTH) of DMT to p‐xylene (PX, ~63% at 240 °C and 16 h) on a reducible ZnZrOx supported Cu catalyst (i.e., Cu/ZnZrOx). Pre‐ and post‐reaction surface and bulk characterization, along with density functional theory (DFT) computations, explicate the dual role of the metal‐support interface of Cu/ZnZrOx in activating both CH3OH and DMT and facilitating a lower free‐energy pathway for both CH3OH dehydrogenation and DMT hydrogenolysis, compared to Cu supported on a redox‐neutral SiO2 support. Loading studies and thermodynamic calculations showed that, under reaction conditions, CH3OH in the gas phase, rather than in the liquid phase, is critical for CTH of DMT. Interestingly, the Cu/ZnZrOx catalyst was also effective for the methanolysis and hydrogenolysis of C‐C bonds (compared to C‐O bonds for PET) of waste polycarbonate (PC), largely forming xylenol (~38%) and methyl isopropyl anisole (~42%) demonstrating the versatility of this approach toward valorizing a wide range of condensation polymers.