We characterize the variation in photometric response of the Dark Energy Camera (DECam) across its 520 Mpix science array during 4 years of operation. These variations are measured using high signal-to-noise aperture photometry of >107 stellar images in thousands of exposures of a few selected fields, with the telescope dithered to move the sources around the array. A calibration procedure based on these results brings the rms variation in aperture magnitudes of bright stars on cloudless nights down to 2-3 mmag, with <1 mmag of correlated photometric errors for stars separated by ≥20″. On cloudless nights, any departures of the exposure zeropoints from a secant airmass law exceeding 1 mmag are plausibly attributable to spatial/temporal variations in aperture corrections. These variations can be inferred and corrected by measuring the fraction of stellar light in an annulus between 6″ and 8″ diameter. Key elements of this calibration include: correction of amplifier nonlinearities; distinguishing pixel-area variations and stray light from quantum-efficiency variations in the flat fields; field-dependent color corrections; and the use of an aperture-correction proxy. The DECam response pattern across the 2° field drifts over months by up to ±9 mmag, in a nearly wavelength-independent low-order pattern. We find no fundamental barriers to pushing global photometric calibrations toward mmag accuracy.