Mehdi Benatia headed an early opener in the seventh minute as Bayern Munich tried to reduce the three-goal deficit against Barcelona.
But Bayern's lead lasted just eight minutes after Neymar capped off a wonderful Barcelona move to level on the night
Jerome Boateng wasn't out quickly enough to prevent Neymar brilliantly scoring again just before the half hour
Robert Lewandowski (left) equalised in the 59th minute but the hosts had given themselves too much to do on aggregate
Thomas Muller netted a second-leg winner in the 74th minute as Bayern Munich didn't go down lightly
Andres Iniesta (top) joins the Barcelona celebrations late as Neymar equalised for the visitors in Germany
Manuel Neuer raises his hand in appealing for offside but to no avail as Neymar tapped home after neat build-up play
Suarez (right) looked pleased as he lapped up the congratulations following Neymar's second goal of the evening.
Messi (right) glides beyond Bayern Munich defender Juan Bernat during a frantic opening half at the Allianz Arena
Brazilian defender Rafinha and Philipp Lahm pay close attention to Barcelona captain Andres Iniesta on Tuesday night
Eccentric German goalkeeper Neuer was at his acrobatic best to deny Neymar a clear run on goal - heading away any danger
Muller balances possession on his head under the watchful eye of Jordi Alba as Bayern tried to find a way back into the game
Bernat on his knees after clearing away a Barcelona attack in which Javier Mascherano had joined in with
Gerard Pique grapples for possession with striker Robert Lewandowski, wearing a mask after breaking his nose