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 milli-magnitudes (mmag), both detections and non-detections with ~2 mmag 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 +/- 1.0 mmag, assuming a Small Magellanic Cloud (SMC) dust extinction law, and it correlates strongly (3.5-sigma) with the metal content, characterised by the SiII1526 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 (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) x 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.
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