We combine photometry of Eris from a 6 month campaign on the Palomar 60 inch telescope in 2015, a 1 month Hubble Space Telescope WFC3 campaign in 2018, and Dark Energy Survey data spanning 2013-2018 to determine a light curve of definitive period 15.771 ± 0.008 days (1σ formal uncertainties), with nearly sinusoidal shape and peak-to-peak flux variation of 3%. This is consistent at part-per-thousand precision with the P = 15.785 90 ± 0.00005 day sidereal period of Dysnomia's orbit around Eris, strengthening the recent detection of synchronous rotation of Eris by Szakáts et al. with independent data. Photometry from Gaia are consistent with the same light curve. We detect a slope of 0.05 ± 0.01 mag per degree of Eris's brightness with respect to illumination phase averaged across g, V, and r bands, intermediate between Pluto's and Charon's values. Variations of 0.3 mag are detected in Dysnomia's brightness, plausibly consistent with a double-peaked light curve at the synchronous period. The synchronous rotation of Eris is consistent with simple tidal models initiated with a giant-impact origin of the binary, but is difficult to reconcile with gravitational capture of Dysnomia by Eris. The high albedo contrast between Eris and Dysnomia remains unexplained in the giant-impact scenario.