Overpressures in sedimentary basins are commonly assumed to be the result of two distinct and separate mechanisms: disequilibrium compaction and fluid expansion. However, the potential for overpressures to be redistributed or transferred to other pressure compartments over time has been seldom considered and rarely demonstrated. Pore-pressure data and velocity-effective stress plots from 61 fields across the Baram Delta province of Brunei (northwest Borneo) reveal that two different types of overpressure occur in stratigraphically defined sections: the basal pro-delta shales contain overpressures generated by disequilibrium compaction, whereas the overlying sand/shale deltaic sequence contains overpressures that appear to be generated by fluid expansion. However, the geology of the deltaic sequences and high magnitude of the pore pressures precludes the overpressures in the deltaic sequences being generated by any conventional fluid expansion mechanism, such as kerogen-to-gas maturation or clay diagenesis. The fluid expansion overpressures are located in fields that were inverted during the Pliocene, an event that resulted in large-scale fluid migration from the pro-delta shales into the deltaic sequences, including charging of the numerous oil fields in the inner shelf. Hence, we propose that the overpressures in Brunei provide the first evidence for a new overpressuring mechanism whereby overpressured fluids have been “vertically transferred” from the pro-delta shales into the deltaic sequences during basin inversion. Furthermore, vertical transfer may be a mechanism for explaining overpressures observed in basins that have been recently uplifted or inverted.