Purple carrot peels are an abundant agro-industrial by-product rich in phytochemicals and have potential applications such as natural colorants and antioxidants. In the context of increasing interest in the valorization of vegetable processing residues, the recovery of bioactive compounds from such materials has become an important scientific and industrial objective. This study aimed to optimize the parameters of a solvent extraction process to maximize total anthocyanin content (TAC), total polyphenol content (TPC), and antioxidant activity (AA) from purple carrot peels. A Central Composite Design, combined with response surface methodology, was used to evaluate the effects of temperature, extraction time, ethanol concentration, and pH across 30 experimental runs. The optimal extraction conditions were identified as pH 4, an ethanol concentration of 50%, a temperature of 80 °C, and an extraction time of 35.88 min. Under the optimized extraction conditions, the experimental values obtained for TAC, TPC, and AA were 2.10 mg C3G/g D.W., 20.60 mg GAE/g D.W, and 19.02 mMol Trolox/g D.W, respectively, which were in close agreement with the predicted values of 2.10 mg C3G/g D.W., 20.30 mg GAE/g D.W, and 19.05 mMol Trolox/g D.W. The good agreement between predicted and experimental values confirmed the adequacy and predictive capability of the developed response surface models. A total of 32 phenolic compounds were characterized by UHPLC–MS/MS, with shikimic acid identified as the dominant compound, highlighting the chemical diversity and abundance of bioactive phenolics in purple carrot peels. The results demonstrate that optimization of extraction parameters significantly enhances the efficiency of conventional solid–liquid extraction, enabling the effective recovery of antioxidant compounds. The proposed approach supports the sustainable valorization of purple carrot by-products as cost-effective sources of natural pigments for food industry applications.