Zika virus (ZIKV) remains a potentially significant public health concern because it can cause teratogenic effects, such as microcephaly in newborns and neurological disease, like Guillain-Barré syndrome. Together with efforts to develop a vaccine, the discovery of antiviral molecules is important to control ZIKV infections and to prevent its most severe symptoms. Here, we report the development of small nonnucleoside inhibitors (NNIs) of ZIKV RNA-dependent RNA polymerase (RdRp) activity. These NNIs target an allosteric pocket (N pocket) located next to a putative hinge region between the thumb and the palm subdomains that was originally described for dengue virus (DENV) RdRp. We first tested the activity of DENV RdRp N-pocket inhibitors against ZIKV RdRp, introduced chemical modifications into these molecules, and assessed their potency using both enzymatic and cell-based assays. The most potent compound had a 50% inhibitory concentration value of 7.3 μM and inhibited ZIKV replication in a cell-based assay with a 50% effective concentration value of 24.3 μM. Importantly, we report four high-resolution crystal structures detailing how these NNIs insert into the N pocket of ZIKV RdRp. Our observations point to subtle differences in the size, shape, chemical environment, and hydration of the N pocket from ZIKV RdRp from those of the N pocket from DENV RdRp that are crucial for the design of improved antiviral inhibitors with activity against ZIKV. IMPORTANCE Zika virus belongs to the Flavivirus genus, which comprises several important human pathogens. There is currently neither an approved vaccine nor antiviral drugs available to prevent infection by ZIKV. The nonstructural protein 5 (NS5) polymerase, which is responsible for replicating the viral RNA genome, represents one of the most promising targets for antiviral drug development. Starting from compounds recently developed against dengue virus NS5, we designed and synthesized inhibitors targeting Zika virus NS5. We show that these novel compounds inhibit viral replication by targeting the polymerase activity. High-resolution X-ray crystallographic structures of protein-inhibitor complexes demonstrated specific binding to an allosteric site within the polymerase, called the N pocket. This work paves the way for the future structure-based design of potent compounds specifically targeting ZIKV RNA polymerase activity.