HIV-1 cores, which contain the viral genome and replication machinery, must disassemble (uncoat) during viral replication. However, the viral and host factors that trigger uncoating remain unidentified. Recent studies show that infectious cores enter the nucleus and uncoat near the site of integration. Here, we show that efficient uncoating of nuclear cores requires synthesis of a double-stranded DNA (dsDNA) genome >3.5 kb and that the efficiency of uncoating correlates with genome size. Core disruption by capsid inhibitors releases viral DNA, some of which integrates. However, most of the viral DNA is degraded, indicating that the intact core safeguards viral DNA. Atomic force microscopy and core content estimation reveal that synthesis of full-length genomic dsDNA induces substantial internal strain on the core to promote uncoating. We conclude that HIV-1 cores protect viral DNA from degradation by host factors and that synthesis of long double-stranded reverse transcription products is required to trigger efficient HIV-1 uncoating.