The dust content of damped Lyman {alpha} systems (DLAs) is an important observable for understanding their origin and the neutral gas reservoirs of galaxies. While the average colour excess of DLAs, E(B-V), is known to be <~15-millimagnitude (mmag), both detections and non-detections with ~2mmag precision have been reported. Here we find 3.2{sigma} statistical evidence for DLA dust-reddening of 774 Sloan Digital Sky Survey (SDSS) quasars by comparing their fitted spectral slopes to those of ~7000 control quasars. The corresponding E(B-V) is 3.0+/-1.0mmag, assuming a Small Magellanic Cloud (SMC) dust extinction law, and it correlates strongly (3.5{sigma}) with the metal content, characterized by the SiII {lambda}1526 absorption-line equivalent width, providing additional confidence that the detection is due to dust in the DLAs. Evolution of E(B-V) over the redshift range 2.1<z<4.0 is limited to <2.5mmag per unit redshift (1{sigma}), consistent with the known, mild DLA metallicity evolution. There is also no apparent relationship with neutral hydrogen column density, N_HI_, though the data are consistent with a mean E(B-V)/N_HI_=(3.5+/-1.0)*10^-24^mag*cm^2^, approximately the ratio expected from the SMC scaled to the lower metallicities typical of DLAs. We implement the SDSS selection algorithm in a portable code to assess the potential for systematic, redshift-dependent biases stemming from its magnitude and colour-selection criteria. The effect on the mean E(B-V) is negligible (<5 per cent) over the entire redshift range of interest. Given the broad potential usefulness of this implementation, we make it publicly available.