We determine the dielectron widths of the Gamma(1S), Gamma(2S), and Gamma(3S) resonances with better than 2% precision by integrating the cross section of e+e- -->Gamma over the e+e- center-of-mass energy. Using e+e- energy scans of the Gamma resonances at the Cornell Electron Storage Ring and measuring Gamma production with the CLEO detector, we find dielectron widths of 1.252+/-0.004(sigma(stat))+/-0.019(sigma(syst)) keV, 0.581+/-0.004+/-0.009 keV, and 0.413+/-0.004+/-0.006 keV for the Gamma(1S), Gamma(2S), and Gamma(3S), respectively.