This article is concerned with the exponential stabilization of a class of linear boundary control systems (BCSs) in port-Hamiltonian form through energy shaping. Starting from a first feedback loop that is in charge of modifying the Hamiltonian function of the plant, a second control loop that guarantees exponential convergence to the equilibrium is designed. In this way, a major limitation of standard energy shaping plus damping injection control laws applied to linear port-Hamiltonian BCSs, namely the fact that only asymptotic convergence is assured, has been removed.