We show how any linear feedback law which asymptotically stabilizes the origin of a linear integrator system of order $(n-1)$ induces a simple continuous time-varying feedback law which exponentially stabilizes the origin of a nonlinear $(2,n)$ single-chain system. The proposed control design method is related to, and extends in the specific case of chained systems, a recent method developed by M'Closkey and Murray \cite{MC.MU3} for driftless systems in order to transform smooth feedback stabilizers yielding slow polynomial convergence into continuous homogeneous ones which ensure faster exponential convergence.