In a search for natural compounds with anti-HIV-1 activity, we studied the effect of the ethanolic extract obtained from leaves, bark, and peels of Punica granatum L. for the inhibition of the HIV-1 reverse transcriptase (RT)-associated ribonuclease H (RNase H) and integrase (IN) LEDGF-dependent activities. The chemical analyses led to the detection of compounds belonging mainly to the phenolic and flavonoid chemical classes. Ellagic acid, flavones, and triterpenoid molecules were identified in leaves. The bark and peels were characterized by the presence of hydrolyzable tannins, such as punicalins and punicalagins, together with ellagic acid. Among the isolated compounds, the hydrolyzable tannins and ellagic acid showed a very high inhibition (IC50 values ranging from 0.12 to 1.4 µM and 0.065 to 0.09 µM of the RNase H and IN activities, respectively). Of the flavonoids, luteolin and apigenin were found to be able to inhibit RNase H and IN functions (IC50 values in the 3.7–22 μM range), whereas luteolin 7-O-glucoside showed selective activity for HIV-1 IN. In contrast, betulinic acid, ursolic acid, and oleanolic acid were selective for the HIV-1 RNase H activity. Our results strongly support the potential of non-edible P. granatum organs as a valuable source of anti-HIV-1 compounds.