Upon treatment removal, spontaneous reactivation of latently infected T cells remains a major barrier toward curing HIV. Therapies that reactivate and clear the latent reservoir are only partially effective, while latency-promoting agents (LPAs) used to suppress reactivation and stabilize latency are understudied and lack diversity in their mechanisms of action. Here, we identify additional LPAs using a screen for gene-expression fluctuations (or “noise”) that drive cell-fate specification and control HIV reactivation from latency. Single-cell protein dynamics of a minimal HIV gene circuit were monitored with time-lapse fluorescence microscopy. We screened 1,806 drugs, out of which 279 modulate noise magnitude or half autocorrelation time. Next, we tested the strongest noise modulators in a Jurkat T cell latency model and discovered three LPAs that would be overlooked by quantifying their mean expression levels alone. The LPAs reduced reactivation of latency in both Jurkat and primary cell models when challenged by synergistic and potent combinations of HIV activators. The two strongest LPAs, NSC 401005 and NSC 400938, are structurally and functionally related to inhibitors of thioredoxin reductase, a protein involved in maintaining redox balance in host cells. Experiments with multiple functional analogs revealed two additional LPAs, PX12 and tiopronin, and suggest a potential LPA family, within which some are commercially available and Food and Drug Administration–approved. The LPAs presented here may provide new strategies to complement antiretroviral treatments. Screening for gene expression noise holds the potential for drug discovery in other diseases.