Suppressing cellular signal transducers of transcription 2 (STAT2) is a common strategy that viruses use to establish infections, yet the detailed mechanism remains elusive, owing to a lack of structural information about the viral-cellular complex involved. Here, we report the cryo-EM and crystal structures of human STAT2 (hSTAT2) in complex with the non-structural protein 5 (NS5) of Zika virus (ZIKV) and dengue virus (DENV), revealing two-pronged interactions between NS5 and hSTAT2. First, the NS5 methyltransferase and RNA-dependent RNA polymerase (RdRP) domains form a conserved interdomain cleft harboring the coiled-coil domain of hSTAT2, thus preventing association of hSTAT2 with interferon regulatory factor 9. Second, the NS5 RdRP domain also binds the amino-terminal domain of hSTAT2. Disruption of these ZIKV NS5-hSTAT2 interactions compromised NS5-mediated hSTAT2 degradation and interferon suppression, and viral infection under interferon-competent conditions. Taken together, these results clarify the mechanism underlying the functional antagonism of STAT2 by both ZIKV and DENV.