Arturo Vidal gave Bayern the lead in the second minute, powerfully heading home a delicious Juan Bernat cross to put the Bundesliga champions in control.
But a second proved elusive, with Jonas twice coming close to equalising and giving Benfica a priceless away goal to take into the return game, which takes place at the Estadio da Luz next Thursday (AEDT).
The Primeira Liga leaders also had a penalty appeal rejected when a cross hit Bayern captain Philipp Lahm on the arm on the box.
Benfica have not reached the semi-finals since the 1989-1990 season and face a tough task to overturn their first-leg defeat, with Bayern seeking a last-four place for the fifth-straight year.
Pep Guardiola's team have now won 11 successive Champions League home games, extending their club record, while Benfica have now failed to beat the Bundesliga champions in seven attempts.
Guardiola had hailed Benfica's defence as the best in Europe before the game, but it took Bayern less than two minutes to break the visitors' resistance.
Bernat delivered a terrific left-wing cross into the box and Vidal made a late run into the box to head home a simple opening goal.
Douglas Costa tested Benfica's goalkeeper Ederson Moraes, who was deputising for injured fellow Brazilian Julio Cesar, after 10 minutes as Bayern dominated the early stages.
Thomas Muller forced another save from Ederson with a volley after 20 minutes, then Benfica had a penalty appeal rejected on a rare attacking foray when a sliding Lahm blocked a cross from close range with his arm.
An inventive chipped free-kick over the wall by Thiago Alcantara almost freed Muller before Vidal planted a header into the ground and just over the crossbar as the one-way traffic continued.
Jonas, who was later booked and will miss the second leg, had Benfica's first shot on target after 55 minutes but it was well dealt with by Manuel Neuer, then Bernat's speculative shot went wide.
The visitors, who had won 19 of their last 20 games in all competitions, were pressing hard and Jonas had a close-range strike well blocked as Rui Vitoria's men sought a crucial away goal.
Ederson denied Franck Ribery with his legs after 80 minutes as Bayern looked to kill the tie off and Benfica could not break down a stubborn Bayern back line, leaving them with a mountain to climb in the second leg.