Rifted margins are formed by persistent stretching of continental lithosphere until breakup is achieved. It is well known that strain-rate-dependent processes control rift evolution, yet quantified extension histories of Earth's major passive margins have become available only recently. Here we investigate rift kinematics globally by applying a new geotectonic analysis technique to revised global plate reconstructions. We find that rifted margins feature an initial, slow rift phase (less than ten millimetres per year, full rate) and that an abrupt increase of plate divergence introduces a fast rift phase. Plate acceleration takes place before continental rupture and considerable margin area is created during each phase. We reproduce the rapid transition from slow to fast extension using analytical and numerical modelling with constant force boundary conditions. The extension models suggest that the two-phase velocity behaviour is caused by a rift-intrinsic strength--velocity feedback, which can be robustly inferred for diverse lithosphere configurations and rheologies. Our results explain differences between proximal and distal margin areas and demonstrate that abrupt plate acceleration during continental rifting is controlled by the nonlinear decay of the resistive rift strength force. This mechanism provides an explanation for several previously unexplained rapid absolute plate motion changes, offering new insights into the balance of plate driving forces through time.