Pancreatic ductal adenocarcinoma (PDAC) is classified into two key subtypes, classical and basal, with basal PDAC predicting worse survival. Using in vitro drug assays, genetic manipulation experiments, and in vivo drug studies in human patient-derived xenografts (PDXs) of PDAC, we found that basal PDACs were uniquely sensitive to transcriptional inhibition by targeting cyclin-dependent kinase 7 (CDK7) and CDK9, and this sensitivity was recapitulated in the basal subtype of breast cancer. We showed in cell lines, PDXs, and publicly available patient datasets that basal PDAC was characterized by inactivation of the integrated stress response (ISR), which leads to a higher rate of global mRNA translation. Moreover, we identified the histone deacetylase sirtuin 6 (SIRT6) as a critical regulator of a constitutively active ISR. Using expression analysis, polysome sequencing, immunofluorescence, and cycloheximide chase experiments, we found that SIRT6 regulated protein stability by binding activating transcription factor 4 (ATF4) in nuclear speckles and protecting it from proteasomal degradation. In human PDAC cell lines and organoids as well as in murine PDAC genetically engineered mouse models where SIRT6 was deleted or down-regulated, we demonstrated that SIRT6 loss both defined the basal PDAC subtype and led to reduced ATF4 protein stability and a nonfunctional ISR, causing a marked vulnerability to CDK7 and CDK9 inhibitors. Thus, we have uncovered an important mechanism regulating a stress-induced transcriptional program that may be exploited with targeted therapies in particularly aggressive PDAC.