We report on a measurement of the Upsilon(1S+2S+3S) -> e+e- cross section at midrapidity in p+p collisions at sqrt(s)=200 GeV. We find the cross section to be 114 +/- 38 (stat.) +23,-24 (syst.) pb. Perturbative QCD calculations at next-to-leading order in the Color Evaporation Model are in agreement with our measurement, while calculations in the Color Singlet Model underestimate it by 2 sigma. Our result is consistent with the trend seen in world data as a function of the center-of-mass energy of the collision and extends the availability of Upsilon data to RHIC energies. The dielectron continuum in the invariant mass range near the Upsilon is also studied to obtain a combined cross section of Drell-Yan plus (b b-bar) -> e+e-.