Arturo Vidal's 38th-minute goal cancelled out the hosts' early lead through Raul Jimenez's header and Thomas Mueller's volley early in the second half eased their nerves.
The Portuguese side, vying for their first semi-final in more than a quarter of a century, managed a late equaliser through Talisca but still suffered their fourth elimination in their fourth European tie against Bayern.
The Bavarians will face Real Madrid, city rivals Atletico, who eliminated holders Barcelona, or England's Manchester City in the last four.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
"It was a sensational atmosphere but it was hard work," said Bayern captain Philipp Lahm, who played his 103rd Champions League game to become joint leader in Germany along with former Bayern keeper Oliver Kahn.
"We had to be more precise than in the first game, close the spaces between midfield and defence and we did it better tonight. We remained calm after the goal and worked hard," said Lahm.
Benfica were without top strikers Jonas, Gaitan and Kostas Mitroglou through suspension or injury and were quickly on the back foot as expected with the Germans controlling 70 percent of possession.
Mueller had the Germans' first good chance but fired wide after 15 minutes with Benfica's double backline working extremely hard.
"That double line was sometimes even three lines. They were a very difficult opponent," said Bayern coach Guardiola.
The hosts struck following a quick break when Eliseu found space to cross from the left and Jimenez charged past two defenders to score with a flying header.
The Mexican went close to adding another but Bayern keeper Manuel Neuer did well to parry his shot.
The Bavarians looked briefly rattled by the setback but quickly recovered when Vidal, who scored the winner in the first leg, drilled in the equaliser after perfectly timing his shot from keeper Ederson's clearance.
Guardiola had surprisingly kept top scorer Robert Lewandowski on the bench and Mueller took over his role, slipping in like a natural centre forward and volleying in a Martinez assist.
Bayern, also chasing a record fourth straight Bundesliga crown as well as the German Cup, did not let up and Douglas Costa' powerful shot hit the post on the hour.
Martinez was lucky not to be sent off for a last-man foul and Benfica coach Rui Vitoria was sent to the stands over the referee's decision to book the Spaniard.
But Talisca gave him something to smile about, curling the resulting free kick past Neuer to cap a battling performance against the German giants.
"We fought until the end, so I have to congratulate my players and these amazing supporters," said the Portuguese coach.
"We faced a very powerful team that knows how to dictate the pace of the game. We promised we would go eye to eye with Bayern and we did so."
(Reporting by Karolos Grohmann, editing by Ed Osmond)
