Rifting between large continental plates results in either continental breakup and the formation of conjugate passive margins, or rift abandonment and a set of aborted rift basins. The nonlinear interaction between key parameters such as plate boundary configuration, lithospheric architecture, and extension geometry determines the dynamics of rift evolution and ultimately selects between successful or failed rifts. In an attempt to evaluate and quantify the contribution of the rift geometry, we analyze the Early Cretaceous extension between Africa and South America that was preceded by ∼20–30 m.y. of extensive intracontinental rifting prior to the final separation between the two plates. While the South Atlantic and Equatorial Atlantic conjugate passive margins continued into seafloor-spreading mode, forming the South Atlantic Ocean basin, Cretaceous African intraplate rifts eventually failed soon after South America broke away from Africa. We investigate the spatiotemporal dynamics of rifting in these domains through a joint plate kinematic and three-dimensional forward numerical modeling approach, addressing (1) the dynamic competition of Atlantic and African extensional systems, (2) two-stage kinematics of the South Atlantic Rift System, and (3) the acceleration of the South America plate prior to final breakup. Oblique rifts are mechanically favored because they require both less strain and less force in order to reach the plastic yield limit. This implies that rift obliquity can act as selector between successful ocean basin formation and failed rifts, explaining the success of the highly oblique Equatorial Atlantic rift and ultimately inhibiting the formation of a Saharan Atlantic Ocean. We suggest that thinning of the last continental connection between Africa and South America produced a severe strength-velocity feedback responsible for the observed increase in South America plate velocity.