Many tissues exhibit subatmospheric interstitial pressures under normal physiologic conditions. The mechanisms by which the lymphatic system extracts fluid from these tissues against the overall pressure gradient are unknown. We address this important physiologic issue by combining experimental measurements of contractile function and pressure generation with a previously validated mathematical model. We provide definitive evidence for the existence of 'suction pressure' in collecting lymphatic vessels, which manifests as a transient drop in pressure downstream of the inlet valve following contraction. This suction opens the inlet valve and is required for filling in the presence of low upstream pressure. Positive transmural pressure is required for this suction, providing the energy required to reopen the vessel. Alternatively, external vessel tethering can serve the same purpose when the transmural pressure is negative. Suction is transmitted upstream, allowing fluid to be drawn in through initial lymphatics. Because suction plays a major role in fluid entry to the lymphatics and is affected by interstitial pressure, our results introduce the phenomenon as another important factor to consider in the study of lymphoedema and its treatment.