Herpes simplex virus 1 (HSV-1) is an important human pathogen and a paradigm for virus-induced host shut-off. Here we show that global changes in transcription and RNA processing and their impact on translation can be analysed in a single experimental setting by applying 4sU-tagging of newly transcribed RNA and ribosome profiling to lytic HSV-1 infection. Unexpectedly, we find that HSV-1 triggers the disruption of transcription termination of cellular, but not viral, genes. This results in extensive transcription for tens of thousands of nucleotides beyond poly(A) sites and into downstream genes, leading to novel intergenic splicing between exons of neighbouring cellular genes. As a consequence, hundreds of cellular genes seem to be transcriptionally induced but are not translated. In contrast to previous reports, we show that HSV-1 does not inhibit co-transcriptional splicing. Our approach thus substantially advances our understanding of HSV-1 biology and establishes HSV-1 as a model system for studying transcription termination.