Motivated by the persistent short-baseline anomalies that hint at the possible existence of physics beyond the standard three-flavor paradigm, we study the phenomenology of light sterile neutrinos in the minimal (3 + 1) framework using two future experiments: the MuOn-decay MEdium-baseline NeuTrino beam experiment (MOMENT) and the Deep Underground Neutrino Experiment (DUNE). We place constraints on active–sterile mixing parameters, probe CP-violation discovery potential, and examine correlations between the standard Dirac CP phase and the additional CP phases arising from active–sterile mixing to quantify phase degeneracies. We present exclusion limits and demonstrate the crucial role of the near detector in improving sensitivities by one or two orders of magnitude compared to a configuration with only the far detector. We find that the presence of sterile neutrinos can reduce the CP-violation sensitivity in long-baseline neutrino oscillation experiments. For large sterile mass splittings, the rapid oscillations average out, leading to strong parameter degeneracies in DUNE. In contrast, MOMENT retains strong sensitivity to CP violation and efficiently disentangles the standard and sterile CP phases. Our results highlight the strong complementarity between DUNE and MOMENT and show that their combined capabilities provide a powerful test of the light sterile neutrino hypothesis in regions of the parameter space that remain weakly constrained by current data.