Context. High-resolution spectroscopy (R ≥ 20 000) at near-infrared wavelengths can be used to investigate the composition, structure, and circulation patterns of exoplanet atmospheres. However, up to now it has been the exclusive dominion of the biggest telescope facilities on the ground, due to the large amount of photons necessary to measure a signal in high-dispersion spectra. Aims. Here we show that spectrographs with a novel design – in particular a large spectral range – can open exoplanet characterisation to smaller telescope facilities too. We aim to demonstrate the concept on a series of spectra of the exoplanet HD 189 733 b taken at the Telescopio Nazionale Galileo with the near-infrared spectrograph GIANO during two transits of the planet. Methods. In contrast to absorption in the Earth’s atmosphere (telluric absorption), the planet transmission spectrum shifts in radial velocity during transit due to the changing orbital motion of the planet. This allows us to remove the telluric spectrum while preserving the signal of the exoplanet. The latter is then extracted by cross-correlating the residual spectra with template models of the planet atmosphere computed through line-by-line radiative transfer calculations, and containing molecular absorption lines from water and methane. Results. By combining the signal of many thousands of planet molecular lines, we confirm the presence of water vapour in the atmosphere of HD 189 733 b at the 5.5σ level. This signal was measured only in the first of the two observing nights. By injecting and retrieving artificial signals, we show that the non-detection on the second night is likely due to an inferior quality of the data. The measured strength of the planet transmission spectrum is fully consistent with past CRIRES observations at the VLT, excluding a strong variability in the depth of molecular absorption lines.