We report the first detection of the second-forbidden, nonunique, 2(+) -> 0(+), ground-state transition in the beta decay of F-20. A low-energy, mass-separated F-20(+) beam produced at the IGISOL facility in Jyvaskyla, Finland, was implanted in a thin carbon foil and the beta spectrum measured using a magnetic transporter and a plastic-scintillator detector. The beta-decay branching ratio inferred from the measurement is b(beta) = [0.41 +/- 0.08(stat) +/- 0.07(sys)] x 10(-5) corresponding to log ft = 10.89(11), making this one of the strongest second-forbidden, nonunique beta transitions ever measured. The experimental result is supported by shell-model calculations and has significant implications for the final evolution of stars that develop degenerate oxygen-neon cores. Using the new experimental data, we argue that the astrophysical electron-capture rate on Ne-20 is now known to within better than 25% at the relevant temperatures and densities.