We present EPISPOT, a fully joint framework which exploits large panels of epigenetic marks as variant-level information to enhance molecular quantitative trait locus (QTL) mapping. Thanks to a purpose-built Bayesian inferential algorithm, our approach effectively couples simultaneous QTL analysis of thousands of genetic variants and molecular traits genome-wide, and hypothesis-free selection of biologically interpretable marks which directly contribute to the QTL effects. This unified learning approach boosts statistical power and sheds light on the regulatory basis of the uncovered associations. EPISPOT is also tailored to the modelling of trans-acting genetic variants, including QTL hotspots, whose detection and functional interpretation are challenging with standard approaches. We illustrate the advantages of EPISPOT in simulations emulating real-data conditions and in an epigenome-driven monocyte expression QTL study which confirms known hotspots and reveals new ones, as well as plausible mechanisms of action. In particular, based on monocyte DNase-I sensitivity site annotations selected by the method from > 150 epigenetic annotations, we clarify the mediation effects and cell-type specificity of well-known master hotspots in the vicinity of the lyzosyme gene. EPISPOT is radically new in that it makes it possible to forgo the daunting and underpowered task of one-mark-at-a-time enrichment analyses for the prioritisation of QTL hits. Our method can be used to enhance the discovery and functional understanding of signals in QTL problems with all types of outcomes, be they transcriptomic, proteomic, lipidomic, metabolic or clinical.