To explore the composition of anthocyanins and expand their biological activities, anthocyanins were systematically isolated and purified from tubers of Solanum tuberosum L., and their tyrosinase inhibitory activity was investigated. In this study, two new anthocyanin degradation compounds, norpetanin (9) and 4-O-(p-coumaryl) rhamnose (10), along with 17 known anthocyanins and their derivatives, were isolated and purified from an acid-ethanolic extract of fresh purple potato tubers. Their structures were elucidated via 1D and 2D NMR and HR-ESI-MS and compared with those reported in the literature. The extracts were evaluated for anthocyanins and their derivatives using a tyrosinase inhibitor screening kit and molecular docking technology, and the results showed that petanin, norpetanin, 4-O-(p-coumaryl) rhamnose, and lyciruthephenylpropanoid D/E possessed tyrosinase inhibitory activity, with 50% inhibiting concentration (IC50) values of 122.37 ± 8.03, 115.53 ± 7.51, 335.03 ± 12.99, and 156.27 ± 11.22 μM (Mean ± SEM, n = 3), respectively. Furthermore, petanin was validated against melanogenesis in zebrafish; it was found that it could significantly inhibit melanin pigmentation (p < 0.001), and the inhibition rate of melanin was 17% compared with the normal group. This finding may provide potential treatments for diseases with abnormal melanin production, and high-quality raw materials for whitening cosmetics.