The mammalian sirtuin, SIRT6, is a key tumor suppressor that maintains genome stability and regulates transcription, though how SIRT6 family members control genome stability is unclear. Here, we use multiple genome-wide approaches to demonstrate that the yeast SIRT6 homologs, Hst3 and Hst4, prevent genome instability by tuning levels of both coding and noncoding transcription. While nascent RNAs are elevated in the absence of Hst3 and Hst4, a global impact on steady-state mRNAs is masked by the nuclear exosome, indicating that sirtuins and the exosome provide two levels of regulation to maintain transcription homeostasis. We find that, in the absence of Hst3 and Hst4, increased transcription is associated with excessive DNA-RNA hybrids (R-loops) that appear to lead to new DNA double-strand breaks. Importantly, dissolution of R-loops suppresses the genome instability phenotypes of hst3 hst4 mutants, suggesting that the sirtuins maintain genome stability by acting as a rheostat to prevent promiscuous transcription.