Steep, rocky landscapes commonly exhibit high sediment yields and are especially sensitive to climate, tectonics, and wildfire. Predicting landscape response to these perturbations demands a quantitative understanding of erosion processes. However, existing models for hillslope sediment production and transport do not apply to landscapes with patchy soil and slopes that exceed the angle for sediment stability. Here we present field measurements in southern California, USA, which indicate that sediment storage on steep slopes is enabled by vegetation that traps sediment upslope. We find that the storage capacity of unburned vegetation dams follows a geometric scaling model with a cubic dependence on effective plant width and an inverse dependence on local slope. Measured sediment volumes behind burned vegetation dams indicate a loss of at least 75% relative to unburned dams, and when expanded to the catchment scale, our measurements match records of postfire sediment yield from nearby retention basins. Contrary to existing models, our observations indicate that wildfire-induced sediment yield is driven by transient storage and release of sediment by vegetation dams, rather than increased bedrock-to-soil conversion rates. Without a feedback between soil production and wildfire, fire may play little role in long-term landscape evolution, and increasing fire frequency in response to climate change may not result in heightened sedimentation hazards due to supply limitations.