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We report J/ψ spectra for transverse momenta pT>5 GeV/c at mid-rapidity in p+p and Au+Au collisions at sNN=200 GeV. The inclusive J/ψ spectrum and the extracted B-hadron feed-down are compared to models incorporating different production mechanisms. We observe significant suppression of the J/ψ yields for pT>5 GeV/c in 0–30% central Au+Au collisions relative to the p+p yield scaled by the number of binary nucleon–nucleon collisions in Au+Au collisions. In 30–60% mid-central collisions, no such suppression is observed. The level of suppression is consistently less than that of high-pTπ± and low-pTJ/ψ at RHIC and high-pTJ/ψ at the LHC.