Scott Parker's men were competing in their first-ever Champions League knockout game, and in truth their inexperience was clear to see as the Primeira Liga leaders ran out as convincing winners despite an energetic start from the hosts.
Benfica had numerous chances to open the scoring before Joao Mario converted from the spot to give the visitors a deserved lead after 50 minutes - the midfielder's fifth goal in this season's Champions League.
The game became stretched as Brugge searched for an equaliser, and the enormous effort the Belgians had exuded was visible when a mistake from Bjorn Meijer allowed David Neres to run through and double Benfica's advantage in the tie late on.
Despite the eventual scoreline, Brugge started the game unlike a team that are sitting in fourth in the Belgian Pro League, with the pace of Noa Lang and Tajon Buchanan giving Benfica plenty to think about in the early stages.
Dutchman Lang managed to get in behind the Benfica defence early on but was unable to convert from a tight angle past Odisseas Vlachodimos.
Benfica began to assert their dominance later in the first half and had numerous chances to go ahead, with the dangerous Rafa Silva hitting the outside of the post following a smart set-piece routine.
Youngster Antonio Silva also had a great opportunity to put the visitors ahead, although the 19-year-old could not keep his header down after centre-back partner Nicolas Otamendi kept the ball alive from a corner.
Despite Benfica's increasing pressure on the hosts' backline, it was Brugge who thought they had opened the scoring just before the interval, however former Fulham man Denis Odoi appeared from an offside position when he headed the ball into the net off teammate Brandon Mechele.
Roger Schmidt's side continued their impressive play after the half-time break, with some neat exchanges between Mario and Silva leading to a cross which prompted Jack Hendry to foul Goncalo Ramos in the area as both raced to the ball.
The aforementioned Mario stepped up and fired his penalty effort at Simon Mignolet, with the 34-year-old only able to parry the powerful strike onto the underside of the bar and into the net.
Substitute Neres strengthened Benfica's position in the tie with a cool finish past Mignolet in the closing stages, although the build-up to the Brazilian's one-on-one chance was entirely avoidable as Meijer's hesitancy handed the 25-year-old a clear run on goal.
Club Brugge have a lot to do in Lisbon next month if they are to advance into the last eight, but must now focus on their faltering Pro League campaign and the fast-approaching derby at Cercle Brugge on Sunday.
Benfica have a trio of Primeira Liga contests before the second-leg clash with Brugge, with the first of those domestic fixtures against Boavista on home soil on Monday evening.