The Belgian underdogs had the brighter start to the tie and opened the deadlock after 15 minutes when Chemsdine Talbi found Ferran Jutgla in a good position to lash past goalkeeper Rui Patricio.
Despite their underwhelming first half, Atalanta managed to go in level at the break after Davide Zappacosta crossed to Mario Pasalic to head home in the 41st minute.
The home team did a great job of keeping the Italian side's attacking line quiet for much of the second period, though La Dea managed to create more danger in the later stages, with Juan Cuadrado seeing a powerful shot saved by Simon Mignolet.
For all their smart passing and dangerous runs at the other end, Club Brugge had difficulty with the final ball whenever they went forward.
However, just when a draw seemed certain, the referee blew for a penalty after a challenge from Isak Hien in stoppage time - much to the defender's outrage. Substitute Gustaf Nilsson stepped up to blast in from the spot to secure the win in the 94th minute.