The South Atlantic rift basin evolved as a branch of a large Jurassic–Cretaceous intraplate rift zone between the African and South American plates during the final break-up of western Gondwana. While the relative motions between South America and Africa for post-break-up times are well resolved, many issues pertaining to the fit reconstruction and particularly the relation between kinematics and lithosphere dynamics during pre-break-up remain unclear in currently published plate models. We have compiled and assimilated data from these intraplated rifts and constructed a revised plate kinematic model for the pre-break-up evolution of the South Atlantic. Based on structural restoration of the conjugate South Atlantic margins and intracontinental rift basins in Africa and South America, we achieve a tight-fit reconstruction which eliminates the need for previously inferred large intracontinental shear zones, in particular in Patagonian South America. By quantitatively accounting for crustal deformation in the Central and West African Rift Zones, we have been able to indirectly construct the kinematic history of the pre-break-up evolution of the conjugate west African–Brazilian margins. Our model suggests a causal link between changes in extension direction and velocity during continental extension and the generation of marginal structures such as the enigmatic pre-salt sag basin and the São Paulo High. We model an initial E–W-directed extension between South America and Africa (fixed in present-day position) at very low extensional velocities from 140 Ma until late Hauterivian times (≈126 Ma) when rift activity along in the equatorial Atlantic domain started to increase significantly. During this initial ≈14 Myr-long stretching episode the pre-salt basin width on the conjugate Brazilian and west African margins is generated. An intermediate stage between ≈126 Ma and base Aptian is characterised by strain localisation, rapid lithospheric weakening in the equatorial Atlantic domain, resulting in both progressively increasing extensional velocities as well as a significant rotation of the extension direction to NE–SW. From base Aptian onwards diachronous lithospheric break-up occurred along the central South Atlantic rift, first in the Sergipe–Alagoas/Rio Muni margin segment in the northernmost South Atlantic. Final break-up between South America and Africa occurred in the conjugate Santos–Benguela margin segment at around 113 Ma and in the equatorial Atlantic domain between the Ghanaian Ridge and the Piauí-Ceará margin at 103 Ma. We conclude that such a multi-velocity, multi-directional rift history exerts primary control on the evolution of these conjugate passive-margin systems and can explain the first-order tectonic structures along the South Atlantic and possibly other passive margins.