Differential cross sections for the reaction $gamma p to p pi^0$ have been measured with the CEBAF Large Acceptance Spectrometer (CLAS) and a tagged photon beam with energies from 0.675 to 2.875 GeV. The results reported here possess greater accuracy in the absolute normalization than previous measurements. They disagree with recent CB-ELSA measurements for the process at forward scattering angles. Agreement with the SAID and MAID fits is found below 1 GeV. The present set of cross sections has been incorporated into the SAID database, and exploratory fits have been extended to 3 GeV. Resonance couplings have been extracted and compared to previous determinations.