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 ¹³CO 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 ¹³CO 10-9 emission and H₂O 1₁₁-0₀₀ 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 ¹³CO and H ₂O lines are confined to ≈ 24" or less. The foreground absorption appears to peak further North than the other components. Radiative transfer models indicate very low abundances of ∼2×10^-10 for H₂O and ∼8×10^-7 for ¹³CO in the dense core, and higher H₂O abundances of ∼4×10^-9 in the foreground cloud and ∼7×10^-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.