The flavivirus nonstructural protein 5 (NS5) performs multiple functions that are essential to viral infection, including replicating and capping the viral RNA and antagonizing the host type I interferon (IFN) response. While flavivirus NS5 proteins inhibit IFN signaling through distinct mechanisms—implying evolutionary flexibility—how these activities coexist and evolve within the same protein remains poorly understood. We mapped the genetic determinants of Zika virus (ZIKV) NS5-mediated STAT2 antagonism and compared them to replication constraints defined by deep mutational scanning (DMS). Antagonism and replication determinants overlapped, and no single amino acid substitution disrupted antagonism without also impairing replication. By resolving both fitness landscapes in parallel, we identified three partially functional substitutions that, when combined, produced replication-competent viruses with markedly reduced IFN antagonism and severe attenuation in a humanized STAT2 mouse model. These findings reveal a fundamental constraint on viral evolution, show how multifunctional viral proteins can limit adaptability—even under immune pressure, and provide the clearest evidence to date that IFN antagonism is essential for in vivo pathogenesis.