The gamma-ray burst GRB 221009A is among the most luminous of its kind and its proximity to Earth has made it an exceptionally rare observational event. The International Gamma-ray Astrophysics Laboratory (INTEGRAL) was in an optimal aspect position to use its all-sky instruments for recording the prompt emission and early gamma-ray afterglow in unprecedented detail. Following the initial detection, a swiftly scheduled follow-up observation allowed for the hard X-ray afterglow time and spectral evolution to be observed for up to almost a week. The INTEGRAL hard X-ray and soft gamma-ray observations have started to bridge the energy gap between the traditionally well-studied soft X-ray afterglow and the high-energy afterglow observed by Fermi/LAT. We discuss the possible implications of these observations for follow-ups of multi-messenger transients with hard X-ray and gamma-ray telescopes.