Helix-distorting DNA lesions, including ultraviolet (UV) light-induced damage, are repaired by the global genomic-nucleotide excision repair (GG-NER) and transcription coupled-nucleotide excision repair (TC-NER) pathways. Previous studies have shown that histone post-translational modifications (PTMs) such as histone acetylation and methylation can promote GG-NER in chromatin. Whether histone PTMs also regulate the repair of DNA lesions by the TC-NER pathway in transcribed DNA is unknown. Here, we report that histone H3 K36 methylation (H3K36me) by the Set2 histone methyltransferase in yeast regulates TC-NER. Mutations in Set2 or H3K36 result in UV sensitivity that is epistatic with Rad26, the primary TC-NER factor in yeast, and cause a defect in the repair of UV damage across the yeast genome. We further show that mutations in Set2 or H3K36 in a GG-NER deficient strain (i.e., rad16Δ) partially rescue its UV sensitivity. Our data indicate that deletion of SET2 rescues UV sensitivity in a GG-NER deficient strain by activating cryptic antisense transcription, so that the non-transcribed strand (NTS) of yeast genes is repaired by TC-NER. These findings indicate that Set2 methylation of H3K36 establishes transcriptional asymmetry in repair by promoting canonical TC-NER of the transcribed strand (TS) and suppressing cryptic TC-NER of the NTS.