We present the mass-metallicity (MZ) and luminosity-metallicity (LZ) relations at z ~ 0.8 from ~1350 galaxies in the Deep Extragalactic Evolutionary Probe 2 survey. We determine stellar masses by fitting the spectral energy distribution inferred from photometry with current stellar population synthesis models. This work raises the number of galaxies with metallicities at z ~0.8 by more than an order of magnitude. We investigate the evolution in the MZ and LZ relations in comparison with local MZ and LZ relations determined in a consistent manner using ~2,000 galaxies in the Sloan Digital Sky Survey. We show that high stellar mass galaxies (M ~ 1010.6 M ) at z ~0.8 have attained the chemical enrichment seen in the local universe, while lower stellar mass galaxies (M ~ 109.2 M ) at z ~0.8 have lower metallicities ( Delta *Dlog(O/H) ~ 0.15 dex) than galaxies at the same stellar mass in the local universe. We find that the LZ relation evolves in both metallicity and B-band luminosity between z ~0.8 and z ~ 0, with the B-band luminosity evolving as a function of stellar mass. We emphasize that the B-band luminosity should not be used as a proxy for stellar mass in chemical evolution studies of star-forming galaxies. Our study shows that both the metallicity evolution and the B-band luminosity evolution for emission-line galaxies between the epochs are a function of stellar mass, consistent with the cosmic downsizing scenario of galaxy evolution.