We address the dynamics of quantum correlations in continuous-variable open systems and analyze the evolution of bipartite Gaussian states in independent noisy channels. In particular, we introduce the notion of dynamical path through a suitable parametrization for symmetric states and focus attention on phenomena that are common to Markovian and non-Markovian Gaussian maps under the assumptions of weak coupling and the secular approximation. We find that the dynamical paths in the parameter space are universal, that is, they depend only on the initial state and on the effective temperature of the environment, with non-Markovianity that manifests itself in the velocity of running over a given path. This phenomenon allows one to map non-Markovian processes onto Markovian ones and may reduce the number of parameters needed to study a dynamical process, e.g., it may be exploited to build constants of motions valid for both Markovian and non-Markovian maps. Universality is also observed in the value of Gaussian discord at the separability threshold, which itself is function of the initial conditions only, in the limit of high temperature. We also prove the existence of excluded regions in the parameter space, i.e., sets of states that cannot be linked by any Gaussian dynamical map.