Alternative splicing of terminal exons increases transcript and protein diversity. How physiological and pathological stimuli regulate the choice between alternative terminal exons is, however, largely unknown. Here, we show that Brahma (BRM), the ATPase subunit of the hSWI/SNF chromatin-remodeling complex interacts with BRCA1/BARD1, which ubiquitinates the 50 kDa subunit of the 3′ end processing factor CstF. This results in the inhibition of transcript cleavage at the proximal poly(A) site and a shift towards inclusion of the distal terminal exon. Upon oxidative stress, BRM is depleted, cleavage inhibition is released, and inclusion of the proximal last exon is favoored. Our findings elucidate a novel regulatory mechanism, distinct from the modulation of transcription elongation by BRM that controls alternative splicing of internal exons. © The Author(s) 2016. Published by Oxford University Press on behalf of Nucleic Acids Research.