Context. Space asteroseismology reveals that stellar structure and evolution models of intermediate- and high-mass stars are in need of improvement in terms of angular momentum and chemical element transport. Aims. We aim to probe the interior structure of a hot, massive star in the core-hydrogen-burning phase of its evolution. Methods. We analysed CoRoT space photometry, Gaia DR2 space astrometry, and high-resolution high signal-to-noise HERMES and HARPS time-series spectroscopy of the slowly rotating B2V star HD 170580. Results. From the time-series spectroscopy, we derive v sin i = 4 ± 2 km s⁻¹, where the uncertainty results from the complex pulsational line-profile variability that has been so far ignored in the literature. We detect 42 frequencies with amplitudes above five times the local noise level. Amongst these we identify five rotationally split triplets and one quintuplet. Asteroseismic modelling based on CoRoT, Gaia DR2, and spectroscopic data leads to a star of M ∼ 8 M_⊙ near core-hydrogen exhaustion and an extended overshoot zone. The detected low-order pressure-mode frequencies cannot be fit within the uncertainties of the CoRoT data by models without atomic diffusion. Irrespective of this limitation, the low-order gravity modes reveal HD 170580 to be a slow rotator with an average rotation period between 73 and 98 d and a hint of small differential rotation. Conclusions. Future Gaia DR3 data taking into account the multiplicity of the star, along with long-term TESS photometry would allow us to put better observational constraints on the asteroseismic models of this blue evolved massive star. Improved modelling with atomic diffusion, including radiative levitation, is needed to achieve compliance with the low helium surface abundance of the star. This poses immense computational challenges but is required to derive the interior rotation and mixing profiles of this star.