The HIV-1 latent reservoir represents an important source of genetic diversity that could contribute to viral evolution and multidrug resistance following latent virus reactivation. This could occur by superinfection of a latently infected cell. We asked whether latent viruses might be reactivated when their host cells are superinfected, and if so, whether they could contribute to the generation of recombinant viruses. Using populations of latently infected Jurkat cells, we found that latent viruses were efficiently reactivated upon superinfection. Pathways leading to latent virus reactivation via superinfection might include gp120-CD4/CXCR4-induced signaling, modulation of the cellular environment by Nef, and/or the activity of Tat produced upon superinfection. Using a range of antiviral compounds and genetic approaches, we show that gp120 and Nef are not required for latent virus reactivation by superinfection, but this process depends on production of functional Tat by the superinfecting virus. In a primary cell model of latency in unstimulated CD4 T cells, superinfection also led to latent virus reactivation. Drug-resistant latent viruses were also reactivated following superinfection in Jurkat cells and were able to undergo recombination with the superinfecting virus. Under drug-selective pressure, this generated multidrug-resistant recombinants that were identified by unique restriction digestion band patterns and by population-level sequencing. During conditions of poor drug adherence, treatment interruption or treatment failure, or in drug-impermeable sanctuary sites, reactivation of latent viruses by superinfection or other means could provide for the emergence or spread of replicatively fit viruses in the face of strong selective pressures.