The torpedo model of transcription termination asserts that the exonuclease Xrn2 attacks the 5′PO₄-end exposed by nascent RNA cleavage and chases down the RNA polymerase. We tested this mechanism using a dominant-negative human Xrn2 mutant and found that it delayed termination genome-wide. Xrn2 nuclease inactivation caused strong termination defects downstream of most poly(A) sites and modest delays at some histone and U snRNA genes, suggesting that the torpedo mechanism is not limited to poly(A) site-dependent termination. A central untested feature of the torpedo model is that there is kinetic competition between the exonuclease and the pol II elongation complex. Using pol II rate mutants, we found that slow transcription robustly shifts termination upstream, and fast elongation extends the zone of termination further downstream. These results suggest that kinetic competition between elongating pol II and the Xrn2 exonuclease is integral to termination of transcription on most human genes.