This letter investigates the dynamic extension of the Controlled Lagrangians methodology for underactuated mechanical systems subject to matched disturbances that depend on the generalized position. A new passivity-preserving controller design procedure is presented for a class of underactuated mechanical systems. An interpretation of the dynamic extension as first-order low-pass filter is proposed. Simulations results on a inertia-wheel pendulum with various types of disturbances demonstrate the effectiveness of the new controller.