We present a joint experimental/theoretical investigation into the roles of spatial structure and time in the competition between two pathogens for a single host. We suggest a natural mechanism by which competing pathogens can coexist when host evolution and competitive dynamics occur on similar time scales. Our experimental system consisted of a single bacterial host species and two competing bacteriophage strains grown on agar plates, with serial transfer of samples of the phage population to fresh host populations after each incubation cycle. The experiments included two incubation times and two transfer protocols that either maintained or disrupted the spatial structure of the viruses at each transfer. The same phage acted as the dominant competitor under both transfer protocols. A striking difference between the treatments is that the weak competitor was able to persist in the long-incubation, but not in the short-incubation experiments. Mathematical and experimental evidence suggest that coexistence is due to the appearance of mutant resistant host cells that provide a transient "spatio-temporal refuge" for the weaker competitor. Our mathematical model is individual based and captures the stochastic spatial dynamics down to the level of individual cells. It produced simulations that were consistent with the behavior seen in the experiments and helped to explain the differences in behavior under the different experimental conditions.