Based on an analysis of the first residues of coupled cluster response functions we devise variational functionals from which the transition moments for n-photon excitations can be calculated as nth derivatives. Combining these functionals with variational perturbation theory, we obtain a new approach for the derivation of multiphoton transition moments which allows us to utilize the full strengths of variational perturbation theory without the roundabout way via residues of response functions. Coupled cluster multiphoton transition moments derived by this approach are formally equivalent to the one identified from the first residues of the ground state response functions. The introduction of the variational functionals makes the mathematical structure of the transition moments more transparent and provides an interpretation of intermediates in terms of responses of excited state vectors and Lagrangian multipliers. 2n + 1 and 2n + 2 rules are formulated for the transition moments and build the basis for a straightforward derivation of a computational efficient formulation. The strength of the new approach is demonstrated by the derivation of three- and four-photon transition moments.