Genotoxic agents, that are used in cancer therapy, elicit the reprogramming of the transcriptome of cancer cells. These changes reflect the cellular response to stress and underlie some of the mechanisms leading to drug resistance. Here, we profiled genome-wide changes in pre-mRNA splicing induced by cisplatin in breast cancer cells. Among the set of cisplatin-induced alternative splicing events we focused on COASY, a gene encoding a mitochondrial enzyme involved in coenzyme A biosynthesis. Treatment with cisplatin induces the production of a short isoform of COASY lacking exons 4 and 5, whose depletion impedes mitochondrial function and decreases sensitivity to cisplatin. We identified RBM39 as a major effector of the cisplatin-induced effect on COASY splicing. RBM39 also controls a genome-wide set of alternative splicing events partially overlapping with the cisplatin-mediated ones. Unexpectedly, inactivation of RBM39 in response to cisplatin involves its interaction with the AP-1 family transcription factor c-Jun that prevents RBM39 binding to pre-mRNA. Our findings therefore uncover a novel cisplatin-induced interaction between a splicing regulator and a transcription factor that has a global impact on alternative splicing and contributes to drug resistance.