We present the first robust evidence of an anticorrelation between the X-ray photon index, Γ, and the X-ray luminosity in a single low-luminosity active galactic nucleus (LLAGN), NGC 7213. Until today, such anticorrelation trends have been seen only in large samples of LLAGN that span a wide range of X-ray fluxes, although the opposite behaviour (i.e. a positive correlation between Γ and X-ray luminosity) has been extensively studied for individual X-ray bright active galactic nuclei. For NGC 7213, we use the long-term X-ray monitoring data of the Rossi X-ray Timing Explorer (RXTE), regularly obtained on average every two days from 2006 March to 2009 December. Based on our X-ray data, we derive the Γ versus flux and the hardness ratio versus flux relations, indicating clearly that NGC 7213 follows a ‘harder when brighter’ spectral behaviour. Additionally, by analysing radio and optical data, and combining data from the literature, we form the most complete spectral energy distribution (SED) of the source across the electromagnetic spectrum yielding a bolometric luminosity of 1.7 × 1043 erg s−1. Phenomenologically, the SED of NGC 7213 is similar to that of a low-ionization nuclear emission-line region. The robust anticorrelation trend that we find between Γ and X-ray luminosity together with the low accretion rate of the source, 0.14 per cent that of the Eddington limit, makes NGC 7213 the first LLAGN exhibiting a similar spectral behaviour with that of black hole X-ray binaries in the ‘hard state’.