Bayern, who had never lost to Benfica in a competitive game before, still qualified as Group C runners-up and will face Brazil’s Flamengo in the knockout stage.
Benfica will face either Chelsea or Esperance from Group D.
With Bayern already sure of their place in the knockout stage, their coach Vincent Kompany made seven changes to his starting line-up and it showed in a sloppy first-half display.
Only goalkeeper Manuel Neuer, defender Josip Stanisic, left-back Raphael Guerreiro and winger Serge Gnabry were kept from the team which beat Boca in the previous game.
Benfica needed a win or a draw to join Bayern in the next round and eliminate Boca Juniors, who were playing Auckland.
The Lisbon side began brightly and Neuer was brought into action early to save a Renato Sanches effort from the edge of the box.
Benfica grabbed the lead in the 13th minute when Fredrik Aursnes got to the byline and pulled the ball back. Norwegian winger Andreas Schjelderup met it with a first-time effort which he buried into the bottom corner.
The game was played in intense heat which had an impact on the tempo of the game, with both teams playing at a slow pace and conserving energy.
Bayern had one opportunity before the break when Gnabry pulled the ball back to Leroy Sane, but the former Manchester City winger fired high over the bar.
Kompany, who knew his side risked losing top spot in the group, had seen enough from his back-up players and made a triple substitution at the break bringing on Harry Kane, Michael Olise and Joshua Kimmich.
Bayern pushed forward in search of a goal that could have sent them back to top of the group but Anatoliy Trubin was out fast to deny Sane and deep in stoppage time Kane mistimed a header from close range. (AFP)