Context. Water is a key molecule in the star formation process, but its spatial distribution in star-forming regions is not well known. Aims. We study the distribution of dust continuum and H2O and (CO)-C-13 line emission in DR21, a luminous star-forming region with a powerful outflow and a compact H II region. Methods. Herschel-HIFI spectra near 1100 GHz show narrow (CO)-C-13 10-9 emission and H2O 1(11)-0(00) absorption from the dense core and broad emission from the outflow in both lines. The H2O line also shows absorption by a foreground cloud known from ground-based observations of low-J CO lines. Results. The dust continuum emission is extended over 36 '' FWHM, while the (CO)-C-13 and H2O lines are confined to approximate to 24 '' or less. The foreground absorption appears to peak further North than the other components. Radiative transfer models indicate very low abundances of similar to 2 x 10(-10) for H2O and similar to 8 x 10(-7) for (CO)-C-13 in the dense core, and higher H2O abundances of similar to 4 x 10(-9) in the foreground cloud and similar to 7 x 10(-7) in the outflow. Conclusions. The high H2O abundance in the warm outflow is probably due to the evaporation of water-rich icy grain mantles, while the H2O abundance is kept down by freeze-out in the dense core and by photodissociation in the foreground cloud.