The dust content of damped Lyman α 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 ∼2 mmag precision have been reported. Here we find 3.2σ 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 ± 1.0 mmag, assuming a Small Magellanic Cloud (SMC) dust extinction law, and it correlates strongly (3.5σ) with the metal content, characterized by the SiII λ1526 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 <2.5 mmag per unit redshift (1σ), consistent with the known, mild DLA metallicity evolution. There is also no apparent relationship with neutral hydrogen column density, NHI, though the data are consistent with a mean E(B−V)/NHI=(3.5±1.0)×10−24 mag cm2, 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.