The structures of novel cocrystals of 4-nitropyridine N-oxide with benzenesulfonamide derivatives, namely, 4-nitrobenzenesulfonamide–4-nitropyridine N-oxide (1/1), C5H4N2O3·C6H6N2O4S, and 4-chlorobenzenesulfonamide–4-nitropyridine N-oxide (1/1), C6H6ClNO2S·C5H4N2O3, are stabilized by N—H…O hydrogen bonds, with the sulfonamide group acting as a proton donor. The O atoms of the N-oxide and nitro groups are acceptors in these interactions. The latter is a double acceptor of bifurcated hydrogen bonds. Previous studies on similar crystal structures indicated competition between these functional groups in the formation of hydrogen bonds, with the priority being for the N-oxide group. In contrast, the present X-ray studies indicate the existence of a hydrogen-bonding synthon including N—H…O(N-oxide) and N—H…O(nitro) bridges. We present here a more detailed analysis of the N-oxide–sulfonamide–nitro N—H…O ternary complex with quantum theory computations and the Quantum Theory of Atoms in Molecules (QTAIM) approach. Both interactions are present in the crystals, but the O atom of the N-oxide group is found to be a more effective proton acceptor in hydrogen bonds, with an interaction energy about twice that of the nitro-group O atoms.