Secondary plant metabolites, e.g., polyphenols, are widely known as health-improving compounds that occur in natural functional foods such as pomegranates. While extracts generated from these fruits inhibit oxidative stress, the allocation of these effects to the different subgroups of substances, e.g., anthocyanins, “copigments” (polyphenols without anthocyanins), or polymeric compounds, is still unknown. Therefore, in the present study, polyphenols from pomegranate juice were extracted and separated into an anthocyanin and copigment fraction using adsorptive membrane chromatography. Phenolic compounds were determined by high performance liquid chromatography with photodiode array (HPLC–PDA) detection and HPLC-PDA electrospray ionization tandem mass spectrometry (HPLC–PDA–ESI–MS/MS), while the free radical scavenging activity of the pomegranate XAD‑7 extract and its fractions was evaluated by the Trolox equivalent antioxidant capacity (TEAC) assay and electron spin resonance (ESR) spectroscopy. Compared to juice, the total phenolic content and free radical scavenging potential was significantly higher in the pomegranate XAD-7 extract and its fractions. In comparison to the anthocyanin and copigment fraction, pomegranate XAD-7 extract showed the highest radical scavenging activity against galvinoxyl and DPPH radicals. Moreover, the enriched XAD-7 extract and its fractions were able to protect human hepatocellular HepG2 cells against oxidative stress induced by hydrogen peroxide. Overall, these results indicated that anthocyanins and copigments act together in reducing oxidative stress.