The Gulf of California rift has accommodated oblique divergence of the Pacific and North America plates in north-western México since Miocene time. Due to its infancy, its rifted margins preserve a rare onshore record of early continental break-up processes and an opportunity to investigate the role of rift obliquity in strain localization. We map rift-related structures and syn-tectonic basins on southern Isla Tiburón, a proximal onshore exposure of the rifted North America margin. We integrate analysis and geochronology of syn-tectonic sedimentary basins and mapping of crosscutting relationships to characterize the style and timing of fault activity. On southern Isla Tiburón, an early phase of extension initiated between~19–17 Ma and ~12.2Ma. Subsequently, these normal faults and related basins were cut by the La Cruz strike-slip fault and buried by deposits of the La Cruz basin, an elongate, fault-controlled trough coextensive with the La Cruz fault. Crosscutting relationships show that the NW-striking La Cruz fault accrued 5 ± 2 km of dextral slip ~8–4 Ma. The La Cruz fault and parallel Tiburón transform were kinematically linked to detachment faulting that accommodated latest Miocene to Pliocene oblique opening of the offshore Upper Tiburón pull-apart basin. The onset of strike-slip faulting on Isla Tiburón was synchronous with the ~8–6 Ma onset of transform faulting and basin formation along >1000 km of the reconstructed Pacific-NorthAmerica plate boundary. This transition coincides with the commencement of a clockwise azimuthal shift in Pacific-North America relative plate motion that increased the obliquity of the Gulf of California rift and formed the Gulf of California shear zone. The record from the proto-Gulf of California illustrates how highly oblique rift geometries, where transform faults are kinematically linked to pull-apart basins, enhance the ability of continental lithosphere to rupture and, ultimately, hasten the formation of new oceanic rift basins.