Ramos, who shot to global fame during the World Cup when he was selected ahead of Cristiano Ronaldo for Portugal and netted a hat-trick against Switzerland, set up the opener for Rafa Silva. The 21-year-old forward then produced two clinical finishes either side of half-time to ensure the two-time European Cup winners would reach the quarter-finals in consecutive seasons.
Joao Mario struck from the spot to score in his fifth consecutive Champions League match - Portugal great Eusebio was the last player to manage the feat for the club. David Neres added the fifth for Benfica before Bjorn Meijer netted a spectacular late consolation. Roger Schmidt's ruthless side finished top of a group containing heavyweights Paris Saint-Germain and Juventus, and made light work of Scott Parker's knock-out stage novices.
Benfica have only been beaten twice all season across all competitions and dominated from the outset against the Belgian visitors. Chiquinho, who has taken Enzo Fernandez's place in midfield after his Premier League record transfer move to Chelsea in January, returned from injury for the hosts. Parker picked Ukrainian striker Roman Yaremchuk against his former side, pairing him with Noa Lang to try and spring an unlikely comeback.
Joao Mario, in sparking goalscoring form this season from midfield, netted after just two minutes with a glorious, flicked finish, but the goal was ruled out for an offside in the build-up. The Portugal midfielder was then foiled by Meijer, who hacked his goal-bound effort off the line. Eventually the hosts took the lead at the Estadio da Luz through Silva after 38 minutes, picked out well in the box by Ramos.
Silva showed good close control to dig out some space and a deft finish to beat former Liverpool goalkeeper Simon Mignolet. Ramos steered home the second just before the break after being teed up by Joao Mario. He netted a brace on Friday against Famalicao to help the Portuguese league leaders maintain an eight-point advantage and was decisive in the box yet again.
Ramos surged inside from the left before firing back across himself into the bottom corner, leaving Mignolet with no chance, notching his 22nd goal of the season across all competitions. Close behind him on 20 is Joao Mario, enjoying the best goalscoring season of his career by a distance. The 30-year-old midfielder slashed a volley narrowly off target early in the second half.
Brugge, who have now won just two of their last 17 games, were a surprise package in the group phase and helped eliminate Atletico Madrid, but were picked apart by the Eagles. Ramos netted his second before the hour mark with a clinical first-time finish from Alex Grimaldo's low cross. Then Joao Mario's coolly taken penalty added sheen to the scoreline after Abakar Sylla clumsily fouled Gilberto.
It was the midfielder's sixth goal of the tournament, pulling him level with Real Madrid's Vinicius Junior as the third top scorer, although five have come from the spot. Neres slotted home the fifth on a bruising night for Parker and his team, who pulled one back through Meijer, as Benfica proved they will be no pushovers in the next round.