Purple passion fruit peel (PPFP) is a waste with high antioxidant capacity. Therefore, in this work, the conditions for solvent extraction of anthocyanins from that peel were studied according to the following variables: temperature, pH, solvent: raw material ratio and time, using the response surface methodology. Additionally, the antioxidant capacity of the extract was characterized, and its respective anthocyanin degradation kinetics were performed at three storage temperatures. The best conditions were pH 2.0, 52.03 °C, 29.79 g of solvent per g of raw material and 180 min, which gave an anthocyanins extraction yield of 577.59 mg of cyanidin-3-O-glucoside per 100 g of dry raw material. The extract also showed 490.12 ± 2.57 and 528.85 ± 27.17 μmol Trolox per 100 g of antioxidant capacity by DPPH and FRAP essays respectively, a low content of vitamin C, as well as activation energy of 41.4 kJ per mole. Consequently, this study shows PPFP as a potential raw material in anthocyanins and antioxidants extracts, which have a great value in the food industry with their stability under refrigeration. Above mentioned displays an alternative strategy for using this waste as a source of high-value products.