Brentford manager Keith Andrew looked to celebrate his new long-term deal with a comfortable win amid a mutinous atmosphere when first-half goals from Damsgaard, Igor Thiago and Kevin Schade put the visitors three up.
Atalanta advanced to the round of 16 by capping an unlikely turnaround when Lazar Samardzic curled a penalty into the top corner in the eighth minute of stoppage time to clinch a 4-1 win on the night and a 4-3 victory on aggregate. Dortmund, the runner-up in 2024, had arrived with a 2-0 lead from the first leg.