We investigated turbulence in 2D atomic Bose-Einstein condensates (BECs) using a minimally destructive, impurity injection technique analogous to particle image velocimetry in conventional fluids. Our approach transfers small regions of the BEC into a different hyperfine state and tracks their displacement, ultimately yielding the velocity field. This allows us to quantify turbulence in the same way as is conventional in fluid dynamics in terms of velocity-velocity correlation functions, called velocity structure functions, that obey Kolmogorov scaling laws. Furthermore, the velocity increments show a clear fat-tail non-Gaussian distribution that results from intermittency corrections to the initial "K41" Kolmogorov theory. Our observations are fully consistent with the later "KO62" description. These results are validated by a 2D dissipative Gross-Pitaevskii simulation.