Therapy resistance is a major clinical problem in cancer medicine and crucial for disease relapse and progression. Therefore, the clinical need to overcome it, particularly for aggressive tumors such as pancreatic cancer, is very high. Aberrant activation of an epithelial-mesenchymal transition (EMT) and an associated cancer stem cell phenotype are considered a major cause of therapy resistance. Particularly, the EMT-activator ZEB1 was shown to confer stemness and resistance. We applied a systematic, stepwise strategy to interfere with ZEB1 function, aiming to overcome drug resistance. This led to the identification of both its target gene miR-203 as a major drug sensitizer and subsequently the class I HDAC inhibitor mocetinostat as epigenetic drug to interfere with ZEB1 function, restore miR-203 expression, repress stemness properties, and induce sensitivity against chemotherapy. Thereby, mocetinostat turned out to be more effective than other HDAC inhibitors, such as SAHA, indicating the relevance of the screening strategy. Our data encourage the application of mechanism-based combinations of selected epigenetic drugs with standard chemotherapy for the rational treatment of aggressive solid tumors, such as pancreatic cancer.