The Integrator complex processes 3'-ends of spliceosomal small nuclear RNAs (snRNAs). Furthermore, it regulates transcription of protein coding genes by terminating transcription after unstable pausing. The molecular basis for Integrator's functions remains obscure. Here, we show that INTS10, Asunder/INTS13 and INTS14 form a separable, functional Integrator module. The structure of INTS13-INTS14 reveals a strongly entwined complex with a unique chain interlink. Unexpected structural homology to the Ku70-Ku80 DNA repair complex suggests nucleic acid affinity. Indeed, the module displays affinity for DNA and RNA but prefers RNA hairpins. While the module plays an accessory role in snRNA maturation, it has a stronger influence on transcription termination after pausing. Asunder/INTS13 directly binds Integrator's cleavage module via a conserved C-terminal motif that is involved in snRNA processing and required for spermatogenesis. Collectively, our data establish INTS10-INTS13-INTS14 as a nucleic acid-binding module and suggest that it brings cleavage module and target transcripts into proximity.