Both canonical and alternative splicing of RNAs are governed by intronic sequence elements and produce transient lariat structures fastened by branch points within introns. To map precisely the location of branch points on a genomic scale, we developed LaSSO (Lariat Sequence Site Origin), a data-driven algorithm which utilizes RNA-seq data. Using fission yeast cells lacking the debranching enzyme Dbr1, LaSSO not only accurately identified canonical splicing events, but also pin-pointed novel, but rare, exon-skipping events, which may reflect aberrantly spliced transcripts. Compromised intron turnover perturbed gene regulation at multiple levels, including splicing and protein translation. Notably, Dbr1 function was also critical for the expression of mitochondrial genes and for the processing of self-spliced mitochondrial introns. LaSSO showed better sensitivity and accuracy than algorithms used for computational branch-point prediction or for empirical branch-point determination. Even when applied to a human data set acquired in the presence of debranching activity, LaSSO identified both canonical and exon-skipping branch points. LaSSO thus provides an effective approach for defining high-resolution maps of branch-site sequences and intronic elements on a genomic scale. LaSSO should be useful to validate introns and uncover branch-point sequences in any eukaryote, and it could be integrated into RNA-seq pipelines.