R-loop disassembly by the human helicase Senataxin contributes to genome integrity and to proper transcription termination at a subset of RNA polymerase II genes. Whether Senataxin also contributes to transcription termination at other classes of genes has remained unclear. Here, we show that Sen1, one of two fission yeast homologues of Senataxin, promotes efficient termination of RNA polymerase III (RNAP3) transcription in vivo. In the absence of Sen1, RNAP3 accumulates downstream of RNAP3-transcribed genes and produces long exosome-sensitive 3'-extended transcripts. Importantly, neither of these defects was affected by the removal of R-loops. The finding that Sen1 acts as an ancillary factor for RNAP3 transcription termination in vivo challenges the pre-existing view that RNAP3 terminates transcription autonomously. We propose that Sen1 is a cofactor for transcription termination that has been co-opted by different RNA polymerases in the course of evolution.