While pressure balance can predict how far the magnetopause will move in response to an upstream pressure change, it cannot determine how fast the transient reponse will be. Using Time History of Events and Macroscale Interactions during Substorms (THEMIS), we present multipoint observations revealing, for the first time, strong (thermal + magnetic) pressure gradients in the magnetosheath due to a foreshock transient, most likely a Hot Flow Anomaly (HFA), which decreased the total pressure upstream of the bow shock. By converting the spacecraft time series into a spatial picture, we quantitatively show that these pressure gradients caused the observed acceleration of the plasma, resulting in fast sunward magnetosheath flows ahead of a localised outward distortion of the magnetopause. The acceleratation of the magnetosheath plasma was fast enough to keep the peak of the magnetopause bulge at approximately the equilibrium position i.e. in pressure balance. Therefore, we show that pressure gradients in the magnetosheath due to transient changes in the total pressure upstream can directly drive anomalous flows and in turn are important in transmitting information from the bow shock to the magnetopause.