The NAC transcription factor (TF) plays a pivotal role in resisting various abiotic stresses, and it has been proved that the overexpression of NAC transcription factors (TFs) in Arabidopsis is beneficial to increase drought tolerance. However, the function of NAC genes in chrysanthemum remains unclear. Here, we conducted physiological and molecular experiments to assess the role of DgNAC1 in response to drought stress of chrysanthemum. DgNAC1-overexpressed chrysanthemum was significantly more drought-resistant than wild type (WT). Especially, the transgenic chrysanthemum presented a greater survival rates (86.42, 88.89 and 87.65%, respectively) than WT (41.98%) under drought conditions. It also showed higher leaf water potential and relative water content; lower relative electrolyte conductivity; fewer accumulations of malondialdehyde, hydrogen peroxide (H2O2), superoxide anion (O2−); higher activities of superoxide dismutase, peroxidase, catalase; and more content of proline, chlorophyll, soluble protein, soluble sugar, glutathione (GSH), glutathione disulphide (GSSG), as well as higher ratio of GSH/GSSG than those of WT during drought stress. Moreover, stress-responsive genes in transgenic chrysanthemum showed a significant up-regulation than in WT under drought stress. Therefore, all the above results suggested that DgNAC1 served as an active regulator in chrysanthemum’s responses to drought stress, and it may have a significant impact on the molecular breeding of drought-resistant plants as well.