The momentum distribution of electrons from decays of heavy flavor (charm and bottom) for midrapidity |y|< 0.35 in p+p collisions at s=200 GeV has been measured by the PHENIX experiment at the BNL Relativistic Heavy Ion Collider over the transverse momentum range 0.3 < p(T)< 9 GeV/c. Two independent methods have been used to determine the heavy-flavor yields, and the results are in good agreement with each other. A fixed-order-plus-next-to-leading-log perturbative QCD calculation agrees with the data within the theoretical and experimental uncertainties, with the data/theory ratio of 1.71 +/- 0.02(stat)+/- 0.18(sys) for 0.3 < p(T)< 9 GeV/c. The total charm production cross section at this energy has also been deduced to be sigma(cc)=567 +/- 57(stat)+/- 193(sys) mu b.