We investigate near-degenerate four-wave mixing in graphene using femtosecond laser pulse shaping microscopy. Intense near-degenerate four-wave mixing signals on either side of the exciting laser spectrum are controlled by amplitude and phase shaping. Quantitative signal modeling for the input pulse parameters shows a spectrally flat phase response of the near-degenerate four-wave mixing due to the linear dispersion of the massless Dirac Fermions in graphene. Exploiting these properties we demonstrate that graphene is uniquely suited for the intrafocus phase characterization and compression of broadband laser pulses, circumventing disadvantages of common methods utilizing second or third harmonic light