Extreme-ultraviolet (EUV) spectroscopy is a very powerful tool that can be used for probing the dynamic response of the solar corona and chromosphere during solar flares. Here we present a unique application of observations from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory using the artifacts of diffraction and dispersion. Using these techniques we can achieve imaging spectroscopy at the resolution of AIA (0farcs6 plate scale) and at the revolutionary cadence of the instrument (nominally 12 s) for the brightest (saturated) pixels during solar flares. Analyzing the dispersion and diffraction effects that are observed as a result of the support grids used for the instrument's front filters, we can achieve up to 0.5 Å spectral resolution across the EUV, optically thin passbands. Here we describe the technique used and present the first result of its application—the emission measure distribution for a single pixel at the top of a flaring loop. We analyze the AIA dispersion spectrum in conjunction with Extreme Ultraviolet Variability Experiment observations and spectroscopic and imaging results from the Reuven Ramaty High Energy Solar Spectroscopic Imager.