Using the approach based on conformal symmetry we calculate the two-loop coefficient function for the axial-vector contributions to two-photon processes in the (MS) over bar scheme. This is the last missing element for the complete next-to-next-to-leading order (NNLO) calculation of the pion transition form factor gamma*gamma -> pi in perturbative QCD. The corresponding high-statistics measurement is planned by the Belle II collaboration and will allow one to put strong constraints on the pion light-cone distribution amplitude. The calculated NNLO corrections prove to be rather large and have to be taken into account. The same coefficient function determines the contribution of the axial-vector generalized parton distributions to deeply virtual Compton scattering (DVCS) which is investigated at the JLAB 12 GeV accelerator, by COMPASS at CERN, and in the future will be studied at the Electron Ion Collider EIC.