An innovative approach to eliminate HIV-1-infected cells emerging out of latency, the major hurdle to HIV-1 cure, is to pharmacologically reactivate viral expression and concomitantly trigger intracellular pro-apoptotic pathways in order to selectively induce cell death (ICD) of infected cells, without reliance on the extracellular immune system. In this work we demonstrate the effect of DEAD-box polypeptide 3, X-Linked (DDX3) inhibitors on selectively inducing cell death in latent HIV-1-infected cell lines, primary CD4+ T cells and in CD4+ T cells from cART-suppressed people living with HIV-1 (PLWHIV). We used single-cell FISH-Flow technology to characterise the contribution of viral RNA to inducing cell death; pharmacological targeting of DDX3 reversed HIV-1 latency and selectively induced apoptosis in viral RNA-expressing CD4+ T cells from PLWHIV but not bystander cells. DDX3 inhibitor treatment of CD4+ T cells from PLWHIV in an in vitro culture model over five days resulted in an approximately 30% reduction of the inducible latent HIV-1 reservoir as determined by quantitation of CA HIV-1 RNA, by TILDA, as well as by FISH-Flow technology. RNA sequencing analysis revealed that while overall gene expression was minimally dysregulated, treatment of independent donor CD4+ T cells with DDX3 inhibitors led to significant downregulation of BIRC5 and HSPB1A, genes critical to cell survival during HIV-1 infection, providing mechanism for the observed selective cell death. Our data support the translation of DDX3 inhibitor class compounds into HIV-1 curative strategies and provide proof of concept for pharmacological reversal of latency coupled to induction of apoptosis towards elimination of the inducible reservoir.