This work optimizes a dynamic vibration absorber (DVA) model equipped with an additional amplifying mechanism using the H∞ optimization criterion, which aims to minimize the maximum frequency response amplitude of the primary structure. This optimization problem is widely investigated using the fixed-point method, which, however, works only when the primary structure is undamped and gives approximate solutions at best. Instead, we seek the exact solutions, and a resultant-based optimization scheme is accordingly proposed, which allows handling purely univariate polynomial equations in the solving procedure to guarantee the convergence and global optimum conditions. Consequently, exactly numerical and closed-form optimal DVA parameters are obtained when the primary structure is damped and undamped, respectively. Furthermore, we are also interested in the effect of the amplifying mechanism on vibration suppression, showing that it functions as a convenient equivalent mass ratio regulator to benefit the DVA performance. Finally, the presented sensitivity analysis reveals the effect of the small variations of the DVA stiffness and damping on the vibration suppression performance and the role of the amplifying mechanism in balancing such two components’ uncertainties. This work generalizes the existing exact H∞ optimization methods and provides a guideline for the enhanced DVA design using the amplifying mechanism.