We calculate shear viscosity and bulk viscosity in SU(3) gauge theory on the lattice at 1.5Tc. The viscosities are extracted via a Kubo formula from the reconstructed spectral function which we determine from the Euclidean time dependence of the corresponding channel of the energy-momentum tensor correlators. We obtain unprecedented precision for the correlators by applying gradient-flow and blocking methods. The correlators are extrapolated to the continuum and then to zero-flow time. To extract the viscosities we fit theoretically inspired models to the lattice data and cross-check the fit results using the Backus-Gilbert method. The final estimates for shear and bulk viscosity are & eta;/s = 0.15-0.48 and & zeta;/s = 0.017-0.059.