Spatial evolution of small perturbations introduced into an inlet cross-section of fully developed turbulent flow in a long straight circular pipe is investigated via direct numerical simulation (DNS). The turbulent inflow field is extracted from an auxiliary streamwise-periodic simulation running in parallel with the main spatial simulation. It is shown that mean perturbation amplitude ϵ increases exponentially with distance downstream. The growth rate is found to be constant when normalized by viscous length, ϵ ~ exp(0.0021x+) over the considered Reynolds-number range 140 ≤ Reτ ≤ 320. The universal character of perturbation growth is confirmed by channel-flow simulations.