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 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. The pharmacological targeting of DDX3 induced HIV-1 RNA expression, resulting in phosphorylation of IRF3 and upregulation of IFNβ. DDX3 inhibition also resulted in the downregulation of BIRC5, critical to cell survival during HIV-1 infection, and selectively induced apoptosis in viral RNA-expressing CD4+ T cells but not bystander cells. DDX3 inhibitor treatment of CD4+ T cells from PLWHIV resulted in an approximately 50% reduction of the inducible latent HIV-1 reservoir by quantitation of HIV-1 RNA, by FISH-Flow, RT-qPCR and TILDA. This study provides proof of concept for pharmacological reversal of latency coupled to induction of apoptosis towards the elimination of the inducible reservoir.