Anthocyanins are attractive alternatives to colorants; however, their low color stability hinders practical application. Copigmentation can enhance both the color intensity and color stability of complexes. Herein, we report an investigation of copigmentation reactions between purple sweet potato anthocyanins (PSA1) and phenolic acids (tannic, ferulic, and caffeic acids) or fatty acids (tartaric and malic acids) at pH 3.5. The effects of the mole ratios of the copigment and the reaction temperature were examined. In addition, quantum mechanical computations were performed to investigate molecular interactions. The optimum PSA:copigment molar ratio was found to be 1:100. The strongest bathochromic and hyperchromic effects were observed for copigmentation with tannic acid (Tan), which might be attributable to the fact that its HOMO-LUMO energy gap was the smallest among the investigated copigments, and because it has a greater number of phenolic aromatic and groups to form more van der Waals and hydrogen bond interactions. However, the formation of the PSA-caffeic acid (Caf) complex was accompanied by the greatest drop in enthalpy (−33.18 kJ/mol) and entropy (−74.55 kJ/mol), and this was the most stable complex at 90 °C. Quantum mechanical calculations indicated that hydrogen bonds and van der Waals force interactions contributed to the color intensification effect of copigmentation. These findings represent an advancement in our understanding of the properties of PSA, expanding the application scope of this natural product.