Protein-coding genes in eukaryotes are transcribed by RNA polymerase II (Pol II) and introns are removed from pre-mRNA by the spliceosome. Understanding the time lag between Pol II progression and splicing could provide mechanistic insights into the regulation of gene expression. Here, we present two single-molecule nascent RNA sequencing methods that directly determine the progress of splicing catalysis as a function of Pol II position. Endogenous genes were analyzed on a global scale in budding yeast. We show that splicing is 50% complete when Pol II is only 45 nt downstream of introns, with the first spliced products observed as introns emerge from Pol II. Perturbations that slow the rate of spliceosome assembly or speed up the rate of transcription caused splicing delays, showing that regulation of both processes determines in vivo splicing profiles. We propose that matched rates streamline the gene expression pathway, while allowing regulation through kinetic competition.