Surface waves process the turbulent disturbances which drive dynamics in many space, astrophysical and laboratory plasma systems, with the outer boundary of Earth’s magnetosphere, the magnetopause, providing an accessible environment to study them. Like waves on water, magnetopause surface waves are thought to travel in the direction of the driving solar wind, hence a paradigm in global magnetospheric dynamics of tailward propagation has been well-established. Here we show through multi-spacecraft observations, global simulations, and analytic theory that the lowest-frequency impulsively-excited magnetopause surface waves, with standing structure along the terrestrial magnetic field, propagate against the flow outside the boundary. Across a wide local time range (09–15h) the waves’ Poynting flux exactly balances the flow’s advective effect, leading to no net energy flux and thus stationary structure across the field also. Further down the equatorial flanks, however, advection dominates hence the waves travel downtail, seeding fluctuations at the resonant frequency which subsequently grow in amplitude via the Kelvin-Helmholtz instability and couple to magnetospheric body waves. This global response, contrary to the accepted paradigm, has implications on radiation belt, ionospheric, and auroral dynamics and potential applications to other dynamical systems.