We consider a class of functional differential equations subject to perturbations, which vary in time, and we study the exponential stability of solutions of these equations using the theory of generalized ordinary differential equations and Lyapunov functionals. We introduce the concept of variational exponential stability for generalized ordinary differential equations and we develop the theory in this direction by establishing conditions for the trivial solutions of generalized ordinary differential equations to be exponentially stable. Then, we apply the results to get corresponding ones for impulsive functional differential equations. We also present an example of a delay differential equation with Perron integrable right-hand side where we apply our result.Univ Estadual Paulista, Dept Matemat, IGCE, BR-13506900 Sao Carlos, SP, BrazilUniv Sao Paulo, Inst Ciencias Matemat & Computacao, BR-13560970 Sao Carlos, SP, BrazilUniv Estadual Paulista, Dept Matemat, IGCE, BR-13506900 Sao Carlos, SP, Brazil