Near-IR and X-ray flares have been detected from the supermassive black hole Sgr A* at the center of our Galaxy with a (quasi)-period of 17-20 minutes, suggesting an emission region only a few Schwarzschild radii above the event horizon. The latest X-ray flare, detected with XMM-Newton, is notable for its detailed lightcurve, yielding not only the highest quality period thus far, but also important structure reflecting the geometry of the emitting region. Recent MHD simulations of Sgr A*'s disk have demonstrated the growth of a Rossby wave instability, that enhances the accretion rate for several hours, possibly accounting for the observed flares. In this Letter, we carry out ray-tracing calculations in a Schwarzschild metric to determine as accurately as possible the lightcurve produced by general relativistic effects during such a disruption. We find that the Rossby wave induced spiral pattern in the disk is an excellent fit to the data, implying a disk inclination angle of 77^o. Note, however, that if this association is correct, the observed period is not due to the underlying Keplerian motion but, rather, to the pattern speed. The favorable comparison between the observed and simulated lightcurves provides important additional evidence that the flares are produced in Sgr A*'s inner disk.