HIV-1 Tat activates viral transcription and limited Tat transactivation correlates with latency establishment. We postulated a "block-and-lock" functional cure approach based on properties of the Tat inhibitor didehydro-Cortistatin A (dCA). HIV-1 transcriptional inhibitors could block ongoing viremia during antiretroviral therapy (ART), locking the HIV promoter in persistent latency. We investigated this hypothesis in human CD4⁺ T cells isolated from aviremic individuals. Combining dCA with ART accelerates HIV-1 suppression and prevents viral rebound after treatment interruption, even during strong cellular activation. We show that dCA mediates epigenetic silencing by increasing nucleosomal occupancy at Nucleosome-1, restricting RNAPII recruitment to the HIV-1 promoter. The efficacy of dCA was studied in the bone marrow-liver-thymus (BLT) mouse model of HIV latency and persistence. Adding dCA to ART-suppressed mice systemically reduces viral mRNA in tissues. Moreover, dCA significantly delays and reduces viral rebound levels upon treatment interruption. Altogether, this work demonstrates the potential of block-and-lock cure strategies.