A significant fraction of stars between 7 and 11 solar masses are thought to become supernovae, but the explosion mechanism is unclear. The answer depends critically on the rate of electron capture on 20Ne in the degenerate oxygen-neon stellar core. However, because of the unknown strength of the transition between the ground states of 20Ne and 20F, it has not previously been possible to fully constrain the rate. By measuring the transition, we establish that its strength is exceptionally large and that it enhances the capture rate by several orders of magnitude. This has a decisive impact on the evolution of the core, increasing the likelihood that the star is (partially) disrupted by a thermonuclear explosion rather than collapsing to form a neutron star. Importantly, our measurement resolves the last remaining nuclear physics uncertainty in the final evolution of degenerate oxygen-neon stellar cores, allowing future studies to address the critical role of convection, which at present is poorly understood.