The emergence of mutations following growth-limiting conditions underlies bacterial drug resistance, viral escape from the immune system and fundamental evolution-driven events. Intriguingly, whether mutations are induced by growth limitation conditions or are randomly generated during growth and then selected by growth limitation conditions remains an open question1. Here, we show that bacteriophage T7 undergoes apparent stress-induced mutagenesis when selected for improved recognition of its host's receptor. In our unique experimental set-up, the growth limitation condition is physically and temporally separated from mutagenesis: growth limitation occurs while phage DNA is outside the host, and spontaneous mutations occur during phage DNA replication inside the host. We show that the selected beneficial mutations are not pre-existing and that the initial slow phage growth is enabled by the phage particle's low-efficiency DNA injection into the host. Thus, the phage particle allows phage populations to initially extend their host range without mutagenesis by virtue of residual recognition of the host receptor. Mutations appear during non-selective intracellular replication, and the frequency of mutant phages increases by natural selection acting on free phages, which are not capable of mutagenesis.