We show that neutral current (NC) measurements at neutrino detectors can play a valuable role in the search for new physics. Such measurements have certain intrinsic features and advantages that can fruitfully be combined with the usual well-studied charged lepton detection channels in order to probe the presence of new interactions or new light states. In addition to the fact that NC events are immune to uncertainties in standard model neutrino mixing and mass parameters, they can have small matter effects and superior rates since all three flavours participate. We also show, as a general feature, that NC measurements provide access to different combinations of CP phases and mixing parameters compared to CC measurements at both long and short baseline experiments. Using the Deep Underground Neutrino Experiment (DUNE) as an illustrative setting, we demonstrate the capability of NC measurements to break degeneracies arising in CC measurements, allowing us, in principle, to distinguish between new physics that violates three flavour unitarity and that which does not. Finally, we show that NC measurements can enable us to restrict new physics parameters that are not easily constrained by CC measurements.