  We consider massless higher-order gravities in general $D=d+1$ dimensions,
which are Einstein gravity extended with higher-order curvature invariants in
such a way that the linearized spectrum around the AdS vacua involves only the
massless graviton. We derive the covariant holographic two-point functions and
find that they have a universal structure. In particular, the theory-dependent
overall coefficient factor $\mathcal{C}_T$ can be universally expressed by
$(d-1) \mathcal{C}_T=\ell (\partial a/\partial\ell)$, where $a$ is the
holographic $a$-charge and $\ell$ is the AdS radius. We verify this relation in
quasi-topological Ricci polynomial, Einstein-Gauss-Bonnet, Einstein-Lovelock
and Einstein cubic gravities. In $d=4$, we also find an intriguing relation
between the holographic $c$ and $a$ charges, namely $c=\frac{1}{3}\ell
(\partial a/\partial \ell)$, which also implies $\mathcal{C}_T=c$.
