We compute three-point correlators between the stress-energy tensor and the conserved currents of conformal field theories (CFTs) in 2+1 dimensions. We first compute the correlators in the large-flavor-number expansion of conformal gauge theories and then perform the computation using holography. In the holographic approach, the correlators are computed from an effective action on (3+1)-dimensional anti-de Sitter space (AdS4) and depend upon the coefficient γ of a four-derivative term in the action. We find a precise match between the CFT and the holographic results, thus, fixing the values of γ. The CFTs of free fermions and bosons take the values γ=1/12,-1/12, respectively, and so saturate the bound |γ|≤1/12 obtained earlier from the holographic theory; the correlator of the conserved gauge flux of U(1) gauge theories takes intermediate values of γ. The value of γ also controls the frequency dependence of the conductivity and other properties of quantum critical transport at nonzero temperatures. Our results for the values of γ lead to an appealing physical interpretation of particlelike or vortexlike transport near quantum phase transitions of interest in condensed-matter physics. This paper includes Appendices reviewing key features of the AdS-CFT correspondence for condensed-matter physicists. © 2013 American Physical Society.