Despite effective antiretroviral therapy, HIV-1-infected cells continue to produce viral antigens and induce chronic immune exhaustion. We propose to identify HIV-1-suppressing agents that can inhibit HIV-1 reactivation and reduce HIV-1-induced immune activation. Using a newly developed dual-reporter system and a high-throughput drug screen, we identified FDA-approved drugs that can suppress HIV-1 reactivation in both cell line models and CD4+ T cells from virally suppressed HIV-1-infected individuals. We identified 11 cellular pathways required for HIV-1 reactivation as druggable targets. Using differential expression analysis, gene set enrichment analysis, and exon-intron landscape analysis, we examined the impact of drug treatment on the cellular environment at a genome-wide level. We identified what we believe to be a new function of a JAK inhibitor, filgotinib, that suppresses HIV-1 splicing. First, filgotinib preferentially suppresses spliced HIV-1 RNA transcription. Second, filgotinib suppresses HIV-1-driven aberrant cancer-related gene expression at the integration site. Third, we found that filgotinib suppresses HIV-1 transcription by inhibiting T cell activation and by modulating RNA splicing. Finally, we found that filgotinib treatment reduces the proliferation of HIV-1-infected cells. Overall, the combination of a drug screen and transcriptome analysis provides systematic understanding of cellular targets required for HIV-1 reactivation and drug candidates that may reduce HIV-1-related immune activation.