We examine the dynamics of the stars and globular clusters in the nearby giant elliptical galaxy M87 and constrain the mass distribution, using all the available data over a large range of radii, including higher order moments of the stellar line-of-sight velocity distributions and the discrete velocities of over 200 globular clusters. We introduce an extension of spherical orbit modeling methods that makes full use of all the information in the data and provides very robust constraints on the mass models. We conclusively rule out a constant mass-to-light ratio model and infer that the radial density profile of the galaxy's dark halo falls off more slowly than r-2, suggesting that the potential of the Virgo Cluster is already dominant at r ~ 300'' ~ 20 kpc.