The abrupt boundary between a magnetosphere and the surrounding plasma, the magnetopause, has long been known to support surface waves. It was proposed that impulses acting on the boundary might lead to a trapping of these waves on the dayside by the ionosphere, resulting in a standing wave or eigenmode of the magnetopause surface. No direct observational evidence of this has been found to date and searches for indirect evidence have proved inconclusive, leading to speculation that this mechanism might not occur. By using fortuitous multipoint spacecraft observations during a rare isolated fast plasma jet impinging on the boundary, here we show that the resulting magnetopause motion and magnetospheric ultra-low frequency waves at well-defined frequencies are in agreement with and can only be explained by the magnetopause surface eigenmode. We therefore show through direct observations that this mechanism, which should impact upon the magnetospheric system globally, does in fact occur.