Trailing 3-0 after the first leg at the Nou Camp, Bayern showed their intention not to give up without a fight with a goal after just seven minutes as Medhi Benatia rose unmarked to head home a corner-kick.
The goal lifted the mood of the home crowd but it was quiet just eight minutes later when a swift Barcelona counter-attack saw Lionel Messi play Luis Suarez in behind the defence, and he squared to Neymar to tap home, 1-1.
Less than 30 minutes gone and it was 2-1 to Barcelona after the same trident combined in almost identical fashion as Neymar took one touch to control before firing low and into the corner at Manuel Neuer's near post.
Just before the hour-mark Robert Lewandowski scored the goal of the game, receiving the ball on the 'D', touching the ball this way, then that, and curling it in off the post, 2-2.
The fightback seemed on in the 74th minute when Thomas Muller curled one into the bottom-right corner from almost the same position as Lewandoskwi's goal following Bastian Schweinsteiger's layoff.
It was now 5-3 on aggregate and Bayern rallied right until the end but ultimately the damage had been done in the first leg, and they were unable to get the goals required despite numerous chances throughout the 90 minutes.
Barcelona will play against the winner between Real Madrid and Juventus, who contest the second leg of their semifinal on Wednesday night with Juve leading 2-1.
