This study identified two phenolic compounds in Schinus terebinthifolius Raddi fruits: naringenin (first report in this species) and gallic acid. Their structures were elucidated by nuclear magnetic resonance (NMR) data (1H-, 13C-NMR) and a high-performance liquid chromatography (HPLC) technique. A high content of phenolics (659.21 mg of gallic acid equivalents/g of sample—Folin-Ciocalteau method) and total flavonoids (140.69 mg of rutin equivalents/g of sample—aluminum chloride method) were quantified in S. terebinthifolius, as well as high antioxidant activity (77.47%—2,2-diphenyl-1-picrylhydrazyl, DPPH method). The antihypertensive activity related to its phenolic content was investigated. After intravenous infusion in Wistar rats, these phenolics significantly reduced (p < 0.05) the systolic, median, and diastolic arterial pressures of individuals. The rotarod test was performed to determine the mechanism of action of the sample vasorelaxant effect. It was found that its action exceeded that of the positive control used (diazepam). This confirmed the vasodilatory activity exerted by S. terebinthifolius fruits is related to the phenolic compounds present in the plant, which are potent antioxidants and inhibit oxidative stress, mainly in the central nervous system.