We present cross section measurements for Z/gamma*+jets+X production, differential in the transverse momenta of the three leading jets. The data sample was collected with the D0 detector at the Fermilab Tevatron proton anti-proton collider at a center-of-mass energy of 1.96 TeV and corresponds to an integrated luminosity of 1 fb-1. Leading and next-to-leading order perturbative QCD predictions are compared with the measurements, and agreement is found within the theoretical and experimental uncertainties. We also make comparisons with the predictions of four event generators. Two parton-shower-based generators show significant shape and normalization differences with respect to the data. In contrast, two generators combining tree-level matrix elements with a parton shower give a reasonable description of the the shapes observed in data, but the predicted normalizations show significant differences with respect to the data, reflecting large scale uncertainties. For specific choices of scales, the normalizations for either generator can be made to agree with the measurements.