Previously considered a neglected flavivirus, Zika virus has recently emerged as a public health concern due to its ability to spread rapidly and cause severe neurological disorders, such as microcephaly in newborn babies from infected mothers, and Guillain-Barré syndrome in adults. Despite extensive efforts towards the identification of effective therapies, specific antivirals are still not available. As part of ongoing medicinal chemistry studies to identify new antiviral agents, we screened against Zika virus replication in vitro in a targeted internal library of small-molecule agents, comprising both nucleoside and non-nucleoside agents. Among the compounds evaluated, novel aryloxyphosphoramidate prodrugs of the nucleosides 2'-C-methyl-adenosine, 2-CMA, and 7-deaza-2'C-methyl-adenosine, 7-DMA, were found to significantly inhibit the virus-induced cytopathic effect in multiple relevant cell lines. In addition, one of these prodrugs exhibits a synergistic antiviral effect against Zika virus when applied in combination with an indirect antiviral agent, a l-dideoxy bicyclic pyrimidine nucleoside analogue, which potently inhibits vaccinia and measles viruses in vitro by targeting a host pathway. Our findings provide a solid basis for further development of an antiviral therapy for Zika virus infections, possibly exploiting a dual approach combining two different agents, one targeting the viral polymerase (direct-acting antiviral), the second targeting a host-directed autophagy mechanism.