The antihypertensive effect of wine lees (WL) has been previously evidenced. In this study, the antihypertensive properties of different doses of WL were evaluated in spontaneously hypertensive rats (SHR). In addition, the blood pressure (BP)-lowering effect of dried (dealcoholized) WL powder (WLPW) and the mechanisms involved in its functionality were investigated. Furthermore, a possible hypotensive effect of WLPW was discarded in Wistar–Kyoto (WKY) rats. The administration of WL at different doses caused a dose-dependent decrease in BP of SHR up to 5.0 mL/kg bw, exhibiting the maximum decrease at 6 h post-administration. WLPW caused a greater drop in BP than WL, showing an antihypertensive effect higher and more prolonged than the drug Captopril. Moreover, the BP-lowering effect of WLPW was specific to the hypertensive state since an undesirable hypotensive effect in normotensive WKY rats was ruled out. Finally, WLPW improved oxidative stress and increased the activity of the antioxidant endogen system of SHR. These results suggest that WLPW could be used as functional ingredient for foods or nutraceuticals to ameliorate hypertension. Nevertheless, further clinical studies are needed to evaluate its long-term antihypertensive efficiency.