From a set of 292 Euphorbiaceae extracts, the use of a molecular networking (MN)-based prioritization approach highlighted three clusters (MN1-3) depicting ions from the bark extract of Codiaeum peltatum. Based on their putative antiviral potential and structural novelty, the MS-guided purification of compounds present in MN1 and MN2 afforded two new daphnane-type diterpenoid orthoesters (DDO), codiapeltines A (1) and B (2), the new actephilols B (3) and C (4), and four known 1,4-dioxane-fused phenanthrene dimers (5-8). The structures of the new compounds were elucidated by NMR spectroscopic data analysis, and the absolute configurations of compounds 1 and 2 were deduced by comparison of experimental and calculated ECD spectra. Codiapeltine B (2) is the first daphnane bearing a 9,11,13-orthoester moiety, establishing a new major structural class of DDO. Compounds 1-8 and four recently reported monoterpenyl quinolones (9-12) detected in MN3 were investigated for their selective activities against chikungunya virus replication and their antipolymerase activities against the NS5 proteins of dengue and zika viruses. Compounds 3-8 exhibited strong inhibitory activities on both dengue and zika NS5 in primary assays, but extensive biological analyses indicated that only actephilol B (3) displayed a specific interaction with the NS5 targets.