Neutral pion and η meson invariant differential yields were measured in non-single diffractive p–Pb collisions at √sNN = 5.02 TeV with the ALICE experiment at the CERN LHC. The analysis combines results from three complementary photon measurements, utilizing the PHOS and EMCal calorimeters and the Photon Conversion Method. The invariant differential yields of π0 and η meson inclusive production are measured near mid-rapidity in a broad transverse momentum range of 0.3 < pT < 20 GeV/c and 0.7 < pT < 20 GeV/c, respectively. The measured η/π0 ratio increases with pT and saturates for pT > 4 GeV/c at 0.483 ± 0.015stat ± 0.015sys. A deviation from mT scaling is observed for pT < 2 GeV/c. The measured η/π0 ratio is consistent with previous measurements from proton-nucleus and pp collisions over the full pT range. The measured η/π0 ratio at high pT also agrees within uncertainties with measurements from nucleus–nucleus collisions. The π0 and η yields in p–Pb relative to the scaled pp interpolated reference, RpPb, are presented for 0.3 < pT < 20 GeV/c and 0.7 < pT < 20 GeV/c, respectively. The results are compared with theoretical model calculations. The values of RpPb are consistent with unity for transverse momenta above 2 GeV/c. These results support the interpretation that the suppressed yield of neutral mesons measured in Pb–Pb collisions at LHC energies is due to parton energy loss in the hot QCD medium.