Pore fluid overpressures in four reservoir sandstones in the Auger Basin, deepwater Gulf of Mexico, are similar across the basin, suggesting that these sandstones are hydraulically connected over distances >20 km. Small overpressure gradients within them suggest upward flow rates between 1 and 20 mm year−1. At the crest of these sandstones, pore pressure equals or exceeds the least principal stress, and we interpret that high fluid pressure is fracturing the caprock and driving flow vertically. A well drilled into the crest of the Auger sandstones confirmed the presence of extreme overpressures that converge on both the least principal stress and the overburden stress. Above these zones, spectacular mud volcanoes are venting fluids today. Overpressured aquifers with significant structural relief may drive fluid vents and mud volcanoes around the world.