Non-coding RNAs (ncRNAs) are frequent and prevalent across the taxa. Although individual non-coding loci have been assigned a function, most are uncharacterized. Their global biological significance is unproven and remains controversial. Here we investigate the role played by ncRNAs in the stress response of Schizosaccharomyces pombe. We integrate global proteomics and RNA sequencing data to identify a systematic programme in which elevated antisense RNA arising both from ncRNAs and from 3'-overlapping convergent gene pairs is directly associated with substantial reductions in protein levels throughout the genome. We describe an extensive array of ncRNAs with trans associations that have the potential to influence multiple pathways. Deletion of one such locus reduces levels of atf1, a transcription factor downstream of the stress-activated mitogen-activated protein kinase (MAPK) pathway, and alters sensitivity to oxidative stress. These non-coding transcripts therefore regulate specific stress responses, adding unanticipated information-processing capacity to the MAPK signalling system.