We propose a new approach to search for light dark matter (DM), with keV-GeV mass, via inelastic nucleus scattering at large-volume neutrino detectors such as Borexino, DUNE, Super-K, Hyper-K, and JUNO. The approach uses inelastic nuclear scattering of cosmic-ray boosted DM, enabling a low-background search for DM in these experiments. Large neutrino detectors, with higher thresholds than dark matter detectors, can be used, since the nuclear deexcitation lines are O(10) MeV. Using a hadrophilic dark-gauge-boson-portal model as a benchmark, we show that the nuclear inelastic channels generally provide better sensitivity than the elastic scattering for a large region of light DM parameter space.