In situ overpressures in sedimentary basins are commonly attributed to disequilibrium compaction or fluid expansion mechanisms, although overpressures in shallow sedimentary sequences may also develop by vertical transfer of pressure from deeper basin levels, for example, via faults. Mafic sill complexes are common features of sedimentary basins at rifted continental margins, often comprising networks of interconnected sills and dikes that facilitate the transfer of magma over considerable vertical distances to shallow basinal depths. Here, we document evidence for deep sills (depths >5 km [>16,000 ft]) hosting permeable, open fracture systems that may have allowed transmission of overpressure from ultradeep basinal (>7 km [>23,000 ft]) levels in the Faroe-Shetland Basin, northeast Atlantic margin. Most notably, well 214/28-1 encountered overpressured, thin (<8 m [<26 ft]), and fractured gas-charged intrusions, which resulted in temporary loss of well control. Although the overpressure could reflect local gas generation related to thermal maturation of Cretaceous shales into which the sills were emplaced, this would require the overpressures to have been sustained for unfeasibly long timescales (>58 m.y.). We instead suggest that transgressive, interconnected sill complexes, such as those penetrated by well 214/28-1, may represent a previously unrecognized mechanism of transferring overpressures (and indeed hydrocarbons) laterally and vertically from deep to shallow levels in sedimentary basins and that they represent a potentially underrecognized hazard to both scientific and petroleum drilling in the vicinity of subsurface igneous complexes.