We study the significance of mergers in the quenching of star formation in galaxies at z ~ 1 by examining their color–mass distributions for different morphology types. We perform two-dimensional light profile fits to GOODS iz images of ~5000 galaxies and X-ray selected active galactic nucleus (AGN) hosts in the CANDELS/GOODS-north and south fields in the redshift range 0.7<z<1.3. Distinguishing between bulge-dominated and disk-dominated morphologies, we find that disks and spheroids have distinct color–mass distributions, in agreement with studies at z ~ 0. The smooth distribution across colors for the disk galaxies corresponds to a slow exhaustion of gas, with no fast quenching event. Meanwhile, blue spheroids most likely come from major mergers of star-forming disk galaxies, and the dearth of spheroids at intermediate green colors is suggestive of rapid quenching. The distribution of moderate luminosity X-ray AGN hosts is even across colors, in contrast, and we find similar numbers and distributions among the two morphology types with no apparent dependence on Eddington ratio. The high fraction of bulge-dominated galaxies that host an AGN in the blue cloud and green valley is consistent with the scenario in which the AGN is triggered after a major merger, and the host galaxy then quickly evolves into the green valley. This suggests AGN feedback may play a role in the quenching of star formation in the minority of galaxies that undergo major mergers.