Seabed-hugging flows called turbidity currents are the volumetrically most important process transporting sediment across our planet and form its largest sediment accumulations. We seek to understand the internal structure and behavior of turbidity currents by reanalyzing the most detailed direct measurements yet of velocities and densities within oceanic turbidity currents, obtained from weeklong flows in the Congo Canyon. We provide a new model for turbidity current structure that can explain why these are far more prolonged than all previously monitored oceanic turbidity currents, which lasted for only hours or minutes at other locations. The observed Congo Canyon flows consist of a short-lived zone of fast and dense fluid at their front, which outruns the slower moving body of the flow. We propose that the sustained duration of these turbidity currents results from flow stretching and that this stretching is characteristic of mud-rich turbidity current systems. The lack of stretching in previously monitored flows is attributed to coarser sediment that settles out from the body more rapidly. These prolonged seafloor flows rival the discharge of the Congo River and carry ~2% of the terrestrial organic carbon buried globally in the oceans each year through a single submarine canyon. Thus, this new structure explains sustained flushing of globally important amounts of sediment, organic carbon, nutrients, and fresh water into the deep ocean.