Using data from the recent BONuS experiment at Jefferson Lab, which utilized a novel spectator tagging technique to extract the inclusive electron-free neutron scattering cross section, we obtain the first direct observation of quark-hadron duality in the neutron F_2 structure function. The data are used to reconstruct the lowest few (N=2, 4 and 6) moments of F_2 in the three prominent nucleon resonance regions, as well as the moments integrated over the entire resonance region. Comparison with moments computed from global parametrizations of parton distribution functions suggest that quark--hadron duality holds locally for the neutron in the second and third resonance regions down to Q^2 ~ 1 GeV^2, with violations possibly up to 20% observed in the first resonance region.