We place empirical constraints on the yields from zero- and low-metallicity core-collapse supernovae (CCSNe) using abundances measured in very metal-poor (VMP; [Fe/H]<=-2) damped Ly{alpha} absorbers (DLAs). For some abundance ratios ([N,Al,S/Fe]), VMP DLAs constrain the metal yields of the first SNe more reliably than VMP stars. We compile a large sample of high-S/N VMP DLAs from over 30yr of literature, most with high-resolution spectral measurements. We infer the initial-mass-function-averaged CCSNe yield from the median values from the DLA abundance ratios of C, N, O, Al, Si, S, and Fe (over Fe and O). We assume that the DLAs are metal-poor enough that they represent galaxies in their earliest stages of evolution, when CCSNe are the only nucleosynthetic sources of the metals we analyze. We compare five sets of zero- and low-metallicity theoretical yields to the empirical yields derived in this work. We find that the five models agree with the DLA yields for ratios containing Si and S. Only one model (HW10; Heger & Woosley 2010ApJ...724..341H) reproduced the DLA values for N, and one other model (LC18; Limongi & Chieffi 2018ApJS..237...13L) reproduced [N/O]. We found little change in the theoretical yields with the adoption of an SN explosion landscape (where certain progenitor masses collapse into black holes, contributing no yields) onto HW10, but fixing explosion energy to progenitor mass results in wide disagreements between the predictions and DLA abundances. We investigate the adoption of a simple, observationally motivated initial distribution of rotational velocities for LC18 and find a slight improvement.