The Transiting Exoplanet Survey Satellite (TESS) will observe ∼150 million stars brighter than , with photometric precision from 60 ppm to 3%, enabling an array of exoplanet and stellar astrophysics investigations. While light curves will be provided for ∼400,000 targets observed at 2 minute cadence, observations of most stars will only be provided as full-frame images (FFIs) at 30 minute cadence. The TESS image scale of ∼21″/pix is highly susceptible to crowding, blending, and source confusion, and the highly spatially variable point-spread function (PSF) will challenge traditional techniques, such as aperture and Gaussian-kernel PSF photometry. We use official "End-to-End 6" TESS simulated FFIs to demonstrate a difference image analysis pipeline, using a δ-function kernel, that achieves the mission specification noise floor of 60 ppm hr−1/2. We show that the pipeline performance does not depend on position across the field, and only ∼2% of stars appear to exhibit residual systematics at the level of ∼5 ppt. We also demonstrate recoverability of planet transits, eclipsing binaries, and other variables. We provide the pipeline as an open-source tool at https://github.com/ryanoelkers/DIA in both IDL and PYTHON. We intend to extract light curves for all point sources in the TESS FFIs as soon as they become publicly available, and will provide the light curves through the Filtergraph data visualization service. An example data portal based on the simulated FFIs is available for inspection at https://filtergraph.com/tess_ffi.