We demonstrate that both Hepatitis C virus (HCV) and Bovine Viral Diarrhea virus (BVDV) contain regions in their 5’ UTRs that stall and repress the enzymatic activity of the cellular 5’-3’ exoribonuclease XRN1, resulting in dramatic changes in the stability of cellular mRNAs. We used biochemical assays, virus infections, and transfection of the HCV and BVDV 5’ untranslated regions in the absence of other viral gene products to directly demonstrate the existence and mechanism of this novel host-virus interaction. In the context of HCV infection, we observed globally increased stability of mRNAs resulting in significant increases in abundance of normally short-lived mRNAs encoding a variety of relevant oncogenes and angiogenesis factors. These findings suggest that non-coding regions from multiple genera of the Flaviviridae interfere with XRN1 and impact post-transcriptional processes, causing global dysregulation of cellular gene expression which may promote cell growth and pathogenesis.