Signaling pathways play a key role in HIV-1 latency. In this study, we used the 24ST1NLESG cell line of HIV-1 latency to screen a library of structurally diverse, medicinally active, cell permeable kinase inhibitors, which target a wide range of signaling pathways, to identify inhibitors of HIV-1 latency reversal. The screen was carried out in the absence or presence of three mechanistically distinct latency-reversing agents (LRAs), namely, prostratin, panobinostat, and JQ-1. We identified inhibitors that only blocked the activity of a specific LRA, as well as inhibitors that blocked the activity of all LRAs. For example, we identified 12 inhibitors targeted toward protein kinase C or downstream kinases that blocked the activity of prostratin. We also identified 12 kinase inhibitors that blocked the reversal of HIV-1 latency irrespective of the LRA used in the screen. Of these, danusertib, an Aurora kinase inhibitor, and PF-3758309, a PAK4 inhibitor, were the most potent. The 50% inhibitory concentrations in the 24ST1NLESG cells ranged from 40 to 147 nM for danusertib (selectivity indices, >150) and from 0.1 to 1 nM for PF-3758309 (selectivity indices, >3,300). Both danusertib and PF-3758309 inhibited latency reversal in CD4⁺ T cells isolated from HIV-1-infected donors. Collectively, our study describes a chemical approach that can be applied to elucidate the role of signaling pathways involved in LRA activity or the maintenance of HIV-1 latency and also identifies inhibitors of latent HIV-1 reactivation that could be used with antiretroviral therapy to reduce residual viremia.