Coherent coupling of Dirac fermion magnetoexcitons with an optical phonon is observed in graphite as marked magnetic-field dependent splittings and anticrossing behavior of the two coupled modes. The sharp magnetophonon resonance occurs in regions of the graphite sample with properties of superior single-layer graphene having enhanced lifetimes of Dirac fermions. The greatly reduced carrier broadening to values below the graphene electron-phonon coupling constant explains the appearance of sharp resonances that reveal a fundamental interaction of Dirac fermions.