A deep observation campaign carried out by the High Energy Stereoscopic System (HESS) on Centaurus A enabled the discovery of γ-rays from the blazar 1ES 1312−423, 2° away from the radio galaxy. With a differential flux at 1 TeV of ϕ(1 TeV) = (1.9 ± 0.6_stat ± 0.4_sys) × 10⁻¹³ cm⁻² s⁻¹ TeV⁻¹ corresponding to 0.5 per cent of the Crab nebula differential flux and a spectral index Γ = 2.9 ± 0.5_stat ± 0.2_sys, 1ES 1312−423 is one of the faintest sources ever detected in the very high energy (E > 100 GeV) extragalactic sky. A careful analysis using three and a half years of Fermi Large Area Telescope (Fermi-LAT) data allows the discovery at high energies (E > 100 MeV) of a hard spectrum (Γ = 1.4 ± 0.4_stat ± 0.2_sys) source coincident with 1ES 1312−423. Radio, optical, UV and X-ray observations complete the spectral energy distribution of this blazar, now covering 16 decades in energy. The emission is successfully fitted with a synchrotron self-Compton model for the non-thermal component, combined with a blackbody spectrum for the optical emission from the host galaxy.