The Zika virus (ZIKV) and dengue virus (DENV) flaviviruses exhibit similar replicative processes but have distinct clinical outcomes. A systematic understanding of virus-host protein-protein interaction networks can reveal cellular pathways critical to viral replication and disease pathogenesis. Here we employed three independent systems biology approaches toward this goal. First, protein array analysis of direct interactions between individual ZIKV/DENV viral proteins and 20,240 human proteins revealed multiple conserved cellular pathways and protein complexes, including proteasome complexes. Second, an RNAi screen of 10,415 druggable genes identified the host proteins required for ZIKV infection and uncovered that proteasome proteins were crucial in this process. Third, high-throughput screening of 6016 bioactive compounds for ZIKV inhibition yielded 134 effective compounds, including six proteasome inhibitors that suppress both ZIKV and DENV replication. Integrative analyses of these orthogonal datasets pinpoint proteasomes as critical host machinery for ZIKV/DENV replication. Our study provides multi-omics datasets for further studies of flavivirus-host interactions, disease pathogenesis, and new drug targets.