We study the mass and anisotropy distribution of the giant elliptical galaxy NGC 5846 using stars, as well as the red and blue globular cluster (GC) subpopulations. We break degeneracies in the dynamical models by taking advantage of the different phase space distributions of the two GC subpopulations to unambiguously constrain the mass of the galaxy and the anisotropy of the GC system. Red GCs show the same spatial distribution and behaviour as the starlight, whereas blue GCs have a shallower density profile, a larger velocity dispersion and a lower kurtosis, all of which suggest a different orbital distribution. We use a dispersion-kurtosis Jeans analysis and find that the solutions of separate analyses for the two GC subpopulations overlap in the halo parameter space. The solution converges on a massive dark matter halo, consistent with expectations from ΛCDM and WMAP7 cosmology in terms of virial mass (logMDM∼13.3Msun) and concentration (cvir∼8). This is the first such analysis that solves the dynamics of the different GC subpopulations in a self-consistent manner. Our method improves the uncertainties on the halo parameter determination by a factor of two and opens new avenues for the use of elliptical galaxy dynamics as tests of predictions from cosmological simulations. The implied stellar mass-to-light ratio derived from the dynamical modelling is fully consistent with a Salpeter initial mass function (IMF) and rules out a bottom light IMF. The different GC subpopulations show markedly distinct orbital distributions at large radii, with red GCs having an anisotropy parameter β∼0.4 outside ∼3Re, and the blue GCs having β∼0.15 at the same radii, while centrally (∼1Re) they are both isotropic. We discuss the implications of our findings within the two-phase formation scenario for early-type galaxies.