Effects of plant treatment with a donor of hydrogen sulfide—sodium hydrosulfide—on the state of antioxidative and osmoprotective systems of young plants of winter wheat (Triticum aestivum L.) cv. Doskonala under conditions of soil drought (progressive decrease in soil moisture down to 25–30% of the total moisture capacity) were studied. Spraying of plants with NaHS solutions (0.1–0.5 mM) before the drought significantly alleviated the growth suppression and favored the conservation of the chlorophyll pool under drought conditions. The beneficial effect of sodium hydrosulfide on plants was eliminated by their simultaneous treatment with hydroxylamine, which is a scavenger of hydrogen sulfide. The plant pretreatment with NaHS prevented the drought-induced accumulation of hydrogen peroxide and that of a lipid peroxidation product (malonic dialdehyde) in leaves. Such pretreatment also promoted an increase in the activity of superoxide dismutase (SOD) and prevented a stress-induced decrease in activities of catalase and guaiacol peroxidase in the leaves. Furthermore, the hydrogen sulfide donor elevated the concentration of proline and considerably increased levels of anthocyanins and UV-absorbing flavonoids under the drought. It is concluded that the plant drought protection afforded by the hydrogen sulfide donor depends to large extent on SOD and flavonoid compounds.