Having come to Munich with a virtually unbeatable 4-0 advantage from the first-leg at the Nou Camp, Barcelona go through 5-1 on aggregate to book their semi-final show-down against Chelsea.
Under-fire Bayern coach Jürgen Klinsmann was not granted the Champions League miracle needed to beat Barcelona, but at least his side earned him a face-saving exit with the draw.
Having been humiliated in last week's first-leg, Bayern would have needed to make Champions League history to reverse a four-goal deficit.
Ribery gave them some faint hope with a 47th minute goal, but Barcelona's Seydou Keita equalised on 73 minutes to end any hope of a fairytale comeback.
"We would have wished for an early goal, then anything would have been possible, but we have lacked the little bit of luck needed," said Klinsmann. "The team has nevertheless given a very good account of themselves against one of the favourites to win the Champions League title."
Having come to Munich with a virtually unbeatable advantage after the Nou Camp rout, Barcelona go through to the semi-finals 5-1 on aggregate.
"We are pleased to be in the semi-finals, we still have a lot of games to get through before we can think of Chelsea," said Barcelona coach Josep Guardiola. "They are a good side, but we need to go and look at the Bayern game first and look at how we played, there are areas to improve."
Barcelona's breath-taking form in the first-leg left them 2-0 up after 12 minutes and Klinsmann says his side were taught a lesson in their quest to defend their Bundesliga crown.
"We have got further than we thought we would, the goal was to reach the last sixteen in the Champions League," added Klinsmann, whose side bounced back with a 4-0 win over Frankfurt in the German league last weekend.
"Now we have to concentrate on the league title and make sure we are German champions again so we can come back to the Champions League next year."
Coming on the back of a 5-1 defeat at Wolfsburg, the 4-0 debacle in Barcelona left Klinsmann's reputation here in tatters and drew much criticism.
Despite leading his country to third place here at the 2006 World Cup, the ex-Germany coach was booed by his own fans before kick-off.
The national papers have been quick to question how long he will last in charge of the German giants and daily newspaper Tageszeitung even printed a front-page image of Klinsmann being crucified in their Easter Sunday edition.
But with his side second in the league, he can ill-afford any more shock results with seven games left this season and a three-point gap to make up on leaders Wolfsburg.