Spatial dynamics can promote persistence of strongly interacting predators and prey. Theory predicts that spatial predator-prey systems are prone to long transients, meaning that the dynamics leading to persistence or extinction manifest over hundreds of generations. Furthermore, the form and duration of transients may be altered by spatial network structure. Few empirical studies have examined the importance of transients in spatial food webs, especially in a network context, due to the difficulty in collecting the large scale and long-term data required. We examined predator-prey dynamics in protist microcosms using three experimental spatial structures: isolated, river-like dendritic networks and regular lattice networks. Densities and patterns of occupancy were followed for both predators and prey over a time scale that equates to >100 predator and >500 prey generations. We found that predators persisted in dendritic and lattice networks whereas they went extinct in the isolated treatment. The dynamics leading to predator persistence played out over long transients with three distinct phases. The transient phases showed differences between dendritic and lattice structures, as did underlying patterns of occupancy. Spatial dynamics differed among organisms in different trophic positions. Predators showed higher local persistence in more connected bottles while prey showed this in more spatially isolated ones. Predictions based on spatial patterns of connectivity derived from metapopulation theory explained predator occupancy, while prey occupancy was better explained by predator occupancy. Our results strongly support the hypothesized role of spatial dynamics in promoting persistence in food webs, but that the dynamics ultimately leading to persistence may occur with long transients which in turn may be influenced by spatial network structure and trophic interactions.