Nuclear export of mRNA is a central step in gene expression that shows extensive coupling to transcription and transcript processing. However, little is known about the fate of mRNA and its export under conditions that damage the DNA template and RNA itself. Here we report the discovery of four new factors required for mRNA export through a screen of all annotated nonessential Saccharomyces cerevisiae genes. Two of these factors, mRNA surveillance factor Rrp6 and DNA repair protein Lrp1, are nuclear exosome components that physically interact with one another. We find that Lrp1 mediates specific mRNA degradation upon DNA-damaging UV irradiation as well as general mRNA degradation. Lrp1 requires Rrp6 for genomic localization to genes encoding its mRNA targets, and Rrp6 genomic localization in turn correlates with transcription. Further, Rrp6 and Lrp1 are both required for repair of UV-induced DNA damage. These results demonstrate coupling of mRNA surveillance to mRNA export and suggest specificity of the RNA surveillance machinery for different transcript populations. Broadly, these findings link DNA and RNA surveillance to mRNA export.