We demonstrate the potential of Euclid’s slitless spectroscopy to discover high-redshift (z > 5) quasars and their main photometric contaminant, ultracool dwarfs. Sensitive infrared spectroscopy from space is able to efficiently identify both populations, as demonstrated by Euclid Near-Infrared Spectrometer and Photometer Red Grism (NISP ${\rm RG}{\scriptscriptstyle \rm E}$) spectra of the newly discovered z = 5.404 quasar EUCL J181530.01+652054.0, as well as several ultracool dwarfs in the Euclid Deep Field North and the Euclid Early Release Observation field Abell 2764. The ultracool dwarfs were identified by cross-correlating their spectra with templates. The quasar was identified by its strong and broad C iii and Mg ii emission lines in the NISP RGE 1206–1892 nm spectrum, and confirmed through optical spectroscopy from the Large Binocular Telescope. The NISP Blue Grism (NISP ${\rm BG}{\scriptscriptstyle \rm E}$) 926–1366 nm spectrum confirms C iv and C iii emission. NISP ${\rm RG}_{\scriptscriptstyle \rm E}$ can find bright quasars at z ≈ 5.5 and z ≳ 7, redshift ranges that are challenging for photometric selection due to contamination from ultracool dwarfs. EUCL J181530.01+652054.0 is a high-excitation, broad absorption line quasar detected at 144 MHz by the LOw-Frequency Array (L144 = 4.0 × 1025 W Hz−1). The quasar has a bolometric luminosity of 3 × 1012 L⊙ and is powered by a 3.4 × 109 M⊙ black hole. The discovery of this bright quasar is noteworthy as fewer than one such object was expected in the ≈20 deg2 surveyed. This finding highlights the potential and effectiveness of NISP spectroscopy in identifying rare, luminous high-redshift quasars, previewing the census of these sources that Euclid’s slitless spectroscopy will deliver over about 14 000 deg2 of the sky.