Although the past epidemic of Zika virus (ZIKV) resulted in severe neurological consequences for infected infants and adults, there are still no approved drugs to treat ZIKV infection. In this study, we applied computational approaches to screen an in-house database of 77 natural and semi-synthetic compounds against ZIKV NS5 RNA-dependent RNA-polymerase (NS5 RdRp), an essential protein for viral RNA elongation during the replication process. For this purpose, we integrated computational approaches such as binding-site conservation, chemical space analysis and molecular docking. As a result, we prioritized nine virtual hits for experimental evaluation. Enzymatic assays confirmed that pedalitin and quercetin inhibited ZIKV NS5 RdRp with IC50 values of 4.1 and 0.5 µM, respectively. Moreover, pedalitin also displayed antiviral activity on ZIKV infection with an EC50 of 19.28 µM cell-based assays, with low toxicity in Vero cells (CC50 = 83.66 µM) and selectivity index of 4.34. These results demonstrate the potential of the natural compounds pedalitin and quercetin as candidates for structural optimization studies towards the discovery of new anti-ZIKV drug candidates.