Quasars are thought to be powered by supermassive black holes accreting surrounding gas. Central to this picture is a putative accretion disk which is believed to be the source of the majority of the radiative output. It is well known, however, that the most extensively studied disk model-an optically thick disk which is heated locally by the dissipation of gravitational binding energy-is apparently contradicted by observations in a few major respects. In particular, the model predicts a specific blue spectral shape asymptotically from the visible to the near-infrared, but this is not generally seen in the visible wavelength region where the disk spectrum is observable. A crucial difficulty has been that, towards the infrared, the disk spectrum starts to be hidden under strong, hot dust emission from much larger but hitherto unresolved scales, and thus has essentially been impossible to observe. Here we report observations of polarized light interior to the dust-emitting region that enable us to uncover this near-infrared disk spectrum in several quasars. The revealed spectra show that the near-infrared disk spectrum is indeed as blue as predicted. This indicates that, at least for the outer near-infrared-emitting radii, the standard picture of the locally heated disk is approximately correct.