Grad-Shafranov (GS) reconstruction is a novel tool for recovering steady two-dimensional (2-D) coherent magnetic field structures from data taken by a single spacecraft. We present first results from a recently developed version of GS reconstruction that incorporates the effects of dynamically significant field-aligned plasma flow. A new GS solver for this case has been developed and is benchmarked with an exact analytical solution. It is then applied to a magnetopause encounter by Cluster 1 (C1) and Cluster 3 (C3) on July 5, 2001. In the C1 crossing, a field-aligned plasma flow, in the frame co-moving with the local magnetopause structures, is present at approximately 57% of the Alfvén speed; in the C3 event the local flow is nearly Alfvénic. We find the following: (1) The recovered field maps are qualitatively similar to those obtained from magneto-hydrostatic GS reconstruction, indicating that the latter can be fairly robust. (2) Our code provides new information about plasma structure and supersonic field-aligned flow effects during reconnection. (3) We confirm results from the previous GS studies of the event, which indicated that significant time evolution occurred in the 30 s time lapse between the two crossings, owing to developing reconnection at a site close to the spacecraft. We provide an estimate of 0.47 mV/m for the reconnection electric field.