Conservation efforts typically focus on maximizing biodiversity in protected areas. The space available for reserves is limited, however, and conservation efforts must increasingly consider how management of protected areas can promote biodiversity beyond reserve borders. Habitat corridors are considered an important feature of reserves because they facilitate movement of organisms between patches, thereby increasing species richness in those patches. Here we demonstrate that by increasing species richness inside target patches, corridors additionally benefit biodiversity in surrounding non-target habitat, a biodiversity "spillover" effect. Working in the world's largest corridor experiment, we show that increased richness extends for approximately 30% of the width of the 1-ha connected patches, resulting in 10-18% more vascular plant species around patches of target habitat connected by corridors than around unconnected but otherwise equivalent patches of habitat. Furthermore, corridor-enhanced spillover into non-target habitat can be predicted by a simple plant life-history trait: seed dispersal mode. Species richness of animal-dispersed plants in non-target habitat increased in response to connectivity provided by corridors, whereas species richness of wind-dispersed plants was unaffected by connectivity and increased in response to changes in patch shape--higher edge-to-interior ratio--created by corridors. Corridors promoted biodiversity spillover for native species of the threatened longleaf pine ecosystem being restored in our experiment, but not for exotic species. By extending economically driven spillover concepts from marine fisheries and crop pollination systems, we show how reconnecting landscapes amplifies biodiversity conservation both within and beyond reserve borders.