The nuclear RNA exosome is an essential multi-subunit complex that controls RNA homeostasis. Congenital mutations in RNA exosome genes are associated with neurodegenerative diseases. Little is known about the role of the RNA exosome in the cellular response to pathogens. Here, using NGS and human and mouse genetics, we show that influenza A virus (IAV) ribogenesis and growth are suppressed by impaired RNA exosome activity. Mechanistically, the nuclear RNA exosome coordinates the initial steps of viral transcription with RNAPII at host promoters. The viral polymerase complex co-opts the nuclear RNA exosome complex and cellular RNAs en route to 3' end degradation. Exosome deficiency uncouples chromatin targeting of the viral polymerase complex and the formation of cellular:viral RNA hybrids, which are essential RNA intermediates that license transcription of antisense genomic viral RNAs. Our results suggest that evolutionary arms races have shaped the cellular RNA quality control machinery.