Atletico got the first proper chance for either side when Giuliano Simeone darted onto the end of a dangerous cross, but Brugge survived the VAR check for a potential foul by the onrushing Simon Mignolet.
It was the goalkeeper in the spotlight again when the hosts found the breakthrough midway through the first half.
Alexander Sorloth showed some nice hold-up play before spinning Brandon Mechele far too easily, and his well-struck shot then somehow contrived to squirm beyond the former Liverpool stopper.
This left a daunting task for Brugge, given that Atletico had kept 13 clean sheets in their last 17 European home knockout matches.
But nobody gave the Belgians that script, and Mechele atoned for his error when he flicked a corner into the path of Joel Ordonez to square the tie up on aggregate for a third time.
And the visitors nearly turned things around completely in the space of two minutes; a teasing cross from Christos Tzolis looked to have set up Hugo Vetlesen, but Jan Oblak produced an excellent save to ensure the sides went in level at half-time.
Moments into the second half, Atleti restored their lead through Johnny Cardoso. His first-ever UCL goal was a special one, leaving Mignolet with no chance this time as the ball flew in from the edge of the box.
The lively Tzolis threatened an instant response, but Oblak was able to hold his swerving long-range effort.
Though Brugge continued to apply pressure, the Slovenian had little else of note to do, although Atleti did have to come through a brief VAR scare of their own after Tzolis saw his progress halted in the box.
Sorloth calmed nerves with his second of the night, applying the finishing touch after Brugge failed to deal with a neat combination between substitutes Ademola Lookman and Antoine Griezmann.
And he completed an impressive hat-trick after being left all alone from a late corner, sealing Atleti’s progression.
Nine of Brugge’s last 10 games have now featured at least three goals, a stat they would probably rather not have extended in the face of Sorloth’s onslaught.
Meanwhile, Atletico Madrid have extended their unbeaten run in regulation time of UCL knockout matches to 20 games (W13, D7). They will go on to face either Liverpool or Tottenham Hotspur in the Round of 16. The draw is scheduled for Friday, with first-leg ties due to be played in March.
Flashcore Man of the Match: Alexander Sorloth (Atleti)
