Cancer-causing herpesviruses infect nearly every human and persist indefinitely in B lymphocytes in a quiescent state known as latency. A hallmark of this quiescence or latency is the presence of extrachromosomal viral genomes with highly restricted expression of viral genes. Silencing of viral genes ensures both immune evasion by the virus and limited pathology to the host, yet how multiple genes on multiple copies of viral genomes are simultaneously silenced is a mystery. In a unifying theme, we report that both cancer-causing human herpesviruses, despite having evolved independently, are silenced through the activities of two members of the Krüppel-associated box (KRAB) domain-zinc finger protein (ZFP) (KRAB-ZFP) epigenetic silencing family, revealing a novel STAT3-KRAB-ZFP axis of virus latency. This dual-edged antiviral strategy restricts the destructive ability of the lytic phase while promoting the cancer-causing latent phase. These findings also unveil roles for KRAB-ZFPs in silencing of multicopy foreign genomes with the promise of evicting herpesviruses to kill viral cancers bearing clonal viral episomes.IMPORTANCE Despite robust immune responses, cancer-causing viruses Epstein-Barr virus (EBV) and Kaposi's sarcoma-associated herpesvirus (KSHV) persist for life. This persistence is accomplished partly through a stealth mechanism that keeps extrachromosomal viral genomes quiescent. Quiescence, or latency, ensures that not every cell harboring viral genomes is killed directly through lytic activation or indirectly via the immune response, thereby evicting virus from host. For the host, quiescence limits pathology. Thus, both virus and host benefit from quiescence, yet how quiescence is maintained through silencing of a large set of viral genes on multiple viral genomes is not well understood. Our studies reveal that members of a gene-silencing family, the KRAB-ZFPs, promote quiescence of both cancer-causing human viruses through simultaneous silencing of multiple genes on multicopy extrachromosomal viral genomes.