The invariant differential cross section for inclusive neutral-pion production in p+p collisions at root s=200 GeV has been measured at midrapidity (\eta\<0.35) over the range 1 < p(T) less than or similar to 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.