  We show that extremal correlators in all Lagrangian ${\cal N}=2$
superconformal field theories with a simple gauge group are governed by the
same universal Toda system of equations, which dictates the structure of
extremal correlators to all orders in the perturbation series. A key point is
the construction of a convenient orthogonal basis for the chiral ring, by
arranging towers of operators in order of increasing dimension, which has the
property that the associated two-point functions satisfy decoupled Toda chain
equations. We explicitly verify this in all known SCFTs based on
$\mathrm{SU}(N)$ gauge groups as well as in superconformal QCD based on
orthogonal and symplectic groups. As a by-product, we find a surprising
non-renormalization property for the ${\cal N}=2$ $\mathrm{SU}(N)$ SCFT with
one hypermultiplet in the rank-2 symmetric representation and one
hypermultiplet in the rank-2 antisymmetric representation, where the two-loop
terms of a large class of supersymmetric observables identically vanish.
