We present a joint theoretical and experimental study of the oxygen K-edge spectra for LaFeO3 and homovalent Ni-substituted LaFeO3 (LaFe0.75Ni0.25O3), using first-principles simulations based on density-functional theory with extended Hubbard functionals and x-ray absorption near edge structure (XANES) measurements. Ground-state and excited-state XANES calculations employ Hubbard onsite U and intersite V parameters determined from first principles and the Lanczos recursive method to obtain absorption cross sections, which allows for a reliable description of XANES spectra in transition-metal compounds in a very broad energy range, with an accuracy comparable to that of hybrid functionals but at a substantially lower cost. We show that standard gradient-corrected exchange-correlation functionals fail in capturing accurately the electronic properties of both materials. In particular, for LaFe0.75Ni0.25O3 they do not reproduce its semiconducting behavior and provide a poor description of the pre-edge features at the O K edge. The inclusion of Hubbard interactions leads to a drastic improvement, accounting for the semiconducting ground state of LaFe0.75Ni0.25O3 and for good agreement between calculated and measured XANES spectra. We show that the partial substitution of Ni for Fe affects the conduction-band bottom by generating a strongly hybridized O(2p)-Ni(3d) minority-spin empty electronic state. The present work, based on a consistent correction of self-interaction errors, outlines the crucial role of extended Hubbard functionals to describe the electronic structure of complex transition-metal oxides such as LaFeO3 and LaFe0.75Ni0.25O3 and paves the way to future studies on similar systems.