The invariant differential cross section for inclusive neutral-pion production in p+p collisions at sqrt[s]=200 GeV has been measured at midrapidity (|eta|<0.35) over the range 1<p(T) less, similar 14 GeV/c by the PHENIX experiment at the Relativistic Heavy Ion Collider. Predictions of next-to-leading order perturbative QCD calculations are consistent with these measurements. The precision of our result is sufficient to differentiate between prevailing gluon-to-pion fragmentation functions.