The process of continental break-up provides a large-scale experiment that can be used to test causal relations between plate tectonics and the dynamics of the Earth's deep mantle. Detailed diagnostic information on the timing and dynamics of such events, which are not resolved by plate kinematic reconstructions, can be obtained from the response of the interior of adjacent continental plates to stress changes generated by plate boundary processes. Here we demonstrate a causal relationship between North Atlantic continental rifting at ~62Myr ago and an abrupt change of the intra-plate deformation style in the adjacent European continent. The rifting involved a left-lateral displacement between the North American-Greenland plate and Eurasia, which initiated the observed pause in the relative convergence of Europe and Africa. The associated stress change in the European continent was significant and explains the sudden termination of a ~20-Myr-long contractional intra-plate deformation within Europe, during the late Cretaceous period to the earliest Palaeocene epoch, which was replaced by low-amplitude intra-plate stress-relaxation features. The pre-rupture tectonic stress was large enough to have been responsible for precipitating continental break-up, so there is no need to invoke a thermal mantle plume as a driving mechanism. The model explains the simultaneous timing of several diverse geological events, and shows how the intra-continental stratigraphic record can reveal the timing and dynamics of stress changes, which cannot be resolved by reconstructions based only on plate kinematics.