Pipes and pipelines are essential for the distribution of fluids, ranging from small diameter tubes in domestic settings to pipes in industrial plants and large scale pipelines. The frictional losses encountered in these flows are responsible for a significant part of the global energy consumption. A huge amount of energy (pumping power due to frictional drag) could be saved if flows in pipes are laminar instead of turbulent. Pipe flow has a property that makes it particularly attractive for control methods which totally extinguish turbulence and establish a laminar flow, as the laminar state is stable to infinitesimal perturbations. Consequently, once relaminarization is achieved, the flow will remain laminar provided that the pipe is straight and smooth. We show that a rather simple, steady perturbation of turbulent flow in a pipe can lead to a complete collapse of turbulence and the flow fully relaminarizes.