We describe the first numerical simulation of continental rifting that reproduces the three major structures observed at magma-poor margins such as the Galicia Margin west of the Iberian Peninsula or the Apulia Margin in the Alps: (1) Distal continental margins consist of fault-bounded blocks separated by oceanward-dipping normal faults. (2) At the tip of the continent, lower crust is scarcely preserved or absent, and upper crust directly overlies exhumed mantle. (3) The base of the rotated crustal blocks is a prominent seismic reflector and represents a high strain zone with a top-to-the-ocean sense of shear. In our model, these structures do not reflect asymmetric rift geometry at a lithospheric scale. Instead, they derive from upper-crustal collapse over a mid-crustal shear zone into the rift center and are present on both sides of the rift axis. The model has a horizontal weak zone in the middle crust on top of strong lower crust and a localized vertical zone of thermal weakness in the rift center. We hypothesize that the development of a thermal perturbation and associated strain localization in the deeper lithosphere may cause the transition from widely distributed faulting and crustal thinning to constricted faulting directed toward a well-defined rift center.