Beam collimation in high-energy colliders is customarily carried out by means of massive amorphous absorbers surrounding the circulating beam. Several studies were performed in the last decades to establish an innovative collimation technique that relies on particle deflection by means of channeling between crystalline planes of a bent crystal. We report the operational use of crystal collimation in the Large Hadron Collider that was achieved during a special high-$β^∗$ physics run with low-intensity beams, representing a milestone for both accelerator and high-energy physics that could pave the way for new synergies in the near future. The deployment of this scheme was steered and motivated by machine-simulation studies, which were then confirmed experimentally using data provided by the experiments thanks to a sensitivity not accessible with the ring instrumentation. The evidence of beam-related experimental background reduction, improved data quality, and faster halo removal with respect to amorphous collimators is obtained using bent crystals as the primary collimation stage. A detailed description of preparatory studies and operational performance is reported, together with a comparison between experimental results and theoretical expectations. Physical review applied 14(6), 064066 (2020). doi:10.1103/PhysRevApplied.14.064066 Published by American Physical Society, College Park, Md. [u.a.]