Using lattice simulations, we measure the sphaleron rate in the Standard Model as a function of temperature through the electroweak cross-over, for the Higgs masses m(H) = 115 and m(H) = 160GeV. We pay special attention to the shutting off of the baryon rate as the temperature is lowered. This quantity enters computations of Baryogenesis via Leptogenesis, where non-zero lepton number is converted into non-zero baryon number by equilibrium sphaleron transitions. Combining existing numerical methods applicable in the symmetric and broken electroweak phases, we find the temperature dependence of the sphaleron rate at very high temperature, through the electroweak cross-over transition, and deep into the broken phase.