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We study correlation functions of spatially separated static quark-antiquark pairs in (2+1)-flavor QCD in order to investigate onset and nature of color screening at high temperatures. We perform lattice calculations in a wide temperature range, 140≤T≤5814 MeV, using the highly improved staggered quark action and several lattice spacings to control discretization effects. By comparing at high temperatures our lattice results to weak-coupling calculations, as well as to the zero temperature result for the energy of a static quark-antiquark pair, we observe that color screening sets in at rT≈0.3. Furthermore, we also observe that in the range 0.3≲rT≲0.6 weak-coupling calculations in the framework of suitable effective field theories provide an adequate picture of color screening.