The sedimentary fill of the Parnaíba basin in NE Brazil is punctuated by two episodes of basaltic magmatism in Jurassic and Cretaceous times, known as the Mosquito and Sardinha formations, respectively. A quantitative understanding of the depth and degree of melting that generated these basalts should provide useful constraints on the history of vertical motions in this cratonic basin. We carried out forward and inverse modelling of major, trace and rare earth element concentrations for primitive melts from both igneous provinces. We calculated the melt fraction as a function of depth to determine the melt volumes and mantle potential temperatures. Our results suggest that both episodes of magmatism resulted from shallow decompression melting within the asthenospheric mantle. The Mosquito basalts record an excess temperature of 55–75°C and are probably related to the widespread Central Atlantic Magmatic Province associated with the initial break-up of Gondwanaland. By contrast, the Sardinha basalts record localized lithospheric thinning to less than half its original thickness with excess temperatures of 15–25°C. This younger activity is probably part of the Paraná–Etendeka large igneous province, which is linked to rifting between South America and Africa. We suspect that these magmatic episodes are associated with phases of regional epeirogenic uplift affecting the Parnaíba basin.