Subvolcanic intrusions in sedimentary basins cause strong thermal perturbations and frequently cause extensive hydrothermal activity. Hydrothermal vent complexes emanating from the tips of transgressive sills are observed in seismic profiles from the Northeast Atlantic margin, and geometrically similar complexes occur in the Stormberg Group within the Late Carboniferous-Middle Jurassic Karoo Basin in South Africa. Distinct features include inward-dipping sedimentary strata surrounding a central vent complex, comprising multiple sandstone dykes, pipes, and hydrothermal breccias. Theoretical arguments reveal that the extent of fluid-pressure build-up depends largely on a single dimensionless number (Ve) that reflects the relative rates of heat and fluid transport. For Ve >> 1, explosive release of fluids from the area near the upper sill surface triggers hydrothermal venting shortly after sill emplacement. In the Karoo Basin, the formation of shallow (< 1 km) sandstone-hosted vents was initially associated with extensive brecciation, followed by emplacement of sandstone dykes and pipes in the central parts of the vent complexes. High fluid fluxes towards the surface were sustained by boiling of aqueous fluids near the sill. Both the sill bodies and the hydrothermal vent complexes represent major perturbations of the permeability structure of the sedimentary basin, and are likely to have long time-scale effects on its hydrogeological evolution.