Among HIV-1 reverse transcriptase (RT)-associated functions, DNA polymerase and Ribonuclease H (RNase H) are both essential for HIV replication and excellent targets for drug development. While all RT inhibitors approved for therapy target the DNA polymerase activity, there is the pressing need for new RT inhibitors possibly targeting the RNase H function. In the last 20 years, many natural substances have shown antiviral activity against HIV-1, but only a few against the RNase H function. In this study, we have tested the ethanolic extracts obtained by the Hypericum hircinum L. (Hypericaceae) growing in Sardinia (Italy) on the HIV-1 RT-associated RNase H function and found that they have inhibitory effects. Active extracts were fractionated up to obtain the main components that have been isolated, tested, and identified to be betulinic acid, shikimic acid, chlorogenic acid, quercetin, 5,7,3′,5′-tetrahydroxyflavanone, and 5,7,3′,5′-tetrahydroxyflavanone 7-O-glucoside. Betulinic acid and 5,7,3′,5′-tetrahydroxyflavanone 7-O-glucoside were active on both RT-associated activities, and betulinic acid was also active on HIV-1 mutant RTs resistant to efavirenz. Overall, our results suggest that some of these compounds inhibit the HIV-1 RT binding to an allosteric site previously described for other natural compounds and are potential leads for further drug development of a single molecules having dual inhibitory activity.