Recent models of South Atlantic opening history focus on early plate divergence by incorporating intracontinental deformation, which is poorly constrained. Aiming to avoid the uncertainties in this approach, we model the entire divergence history with a joint inversion for seafloor spreading data. For this history, the pre-Campanian motion parameters are the first to feature formal uncertainty estimates. We date the onset of spreading at 138 Ma, with movement along intracontinental accommodation zones leading to the assembly of South America by 123 Ma and Africa by 106 Ma. Part of the ridge in the Agulhas Basin jumped westward soon afterward toward the Bouvet plume, initiating the motion of a short-lived Malvinas Plate. The NE Georgia and Maud rises and Agulhas Plateau formed as a large igneous province over the plume. Farther north, part of the ridge jumped eastward toward the Tristan plume around 94–93 Ma but seems not to have resulted in independent plate motion. Our results show that the South Atlantic grew by diachronous breakup of continents on just two plates. Cretaceous intracontinental deformation in South America and Africa can be interpreted in terms of the accommodation of stress associated with northward propagation of this process. The pattern of accommodation is usually envisaged as focusing all of the strain in narrow belts. With our rotations, a commonly used set of such belts accounts instead for just 42–67% of the implied total strain. We suggest that the remainder was accommodated at all scales within the continental interiors and the extended continental margins.