We present a NuSTAR and XMM–Newton monitoring campaign in 2014/2015 of the Compton-thick Seyfert 2 galaxy, NGC 1068. During the 2014 August observation, we detect with NuSTAR a flux excess above 20 keV (32 ± 6 per cent) with respect to the 2012 December observation and to a later observation performed in 2015 February. We do not detect any spectral variation below 10 keV in the XMM–Newton data. The transient excess can be explained by a temporary decrease of the column density of the obscuring material along the line of sight (from N H ≃ 1025 cm−2 to N H = 6.7 ± 1.0 × 1024 cm−2), which allows us for the first time to unveil the direct nuclear radiation of the buried active galactic nucleus in NGC 1068 and to infer an intrinsic 2–10 keV luminosity L $_{\rm X}=7^{+7}_{-4} \times 10^{43}$  erg s−1.