Previous observations have shown a ∼10–15 min time delay in the ionospheric response to solar wind directional discontinuities marked by either southward or northward interplanetary magnetic field (IMF) turnings. We have studied one southward IMF turning observed by Time History of Events and Macroscale Interactions during Substorms (THEMIS) and GOES in the dayside magnetosphere. Using a global MHD model, we have reproduced the magnetopause motion in this event. We find that the observed delay in the ground response can be completely explained by deceleration of the directional discontinuity in the subsolar magnetosheath. We show that the speed of the discontinuity significantly decreases in the vicinity of the magnetopause where the magnetic barrier formed during the previous northward IMF interval. The southward turning can reach the magnetopause only after complete disruption of the magnetic barrier. The disruption or dissipation occurs via magnetosheath reconnection, as confirmed by high-speed jets in the magnetosheath. The magnetopause moves sunward as the directional discontinuity transits the magnetosheath. This sunward motion is followed by the earthward motion when the discontinuity strikes the magnetopause and magnetopause reconnection begins.