Double-stranded DNA ends, often from replication, drive genomic instability, yet their origin in non-replicating cells is unknown. Here we show that transcriptional RNA/DNA hybrids (R-loops) generate DNA ends that underlie stress-induced mutation and amplification. Depleting RNA/DNA hybrids with overproduced RNase HI reduces both genomic changes, indicating RNA/DNA hybrids as intermediates in both. An Mfd requirement and inhibition by translation implicate transcriptional R-loops. R-loops promote instability by generating DNA ends, shown by their dispensability when ends are provided by I-SceI endonuclease. Both R-loops and single-stranded endonuclease TraI are required for end formation, visualized as foci of a fluorescent end-binding protein. The data suggest that R-loops prime replication forks that collapse at single-stranded nicks, producing ends that instigate genomic instability. The results illuminate how DNA ends form in non-replicating cells, identify R-loops as the earliest known mutation/amplification intermediate, and suggest that genomic instability during stress could be targeted to transcribed regions, accelerating adaptation.