Jupp Heynckes' men produced another top-class performance to record a 7-0 aggregate over the Catalan giants following their powerful 4-0 triumph in Munich last week.
The breakthrough for Bayern came three minutes into the second half when Robben raced onto a long ball from David Alaba, taking possession on the right, before cutting back into the area and placing a perfect left-footed effort to the right of Victor Valdes and into the back of the net.
That preceded the second goal in the 72nd minute when Franck Ribery broke down the left and sent in a dangerous ball which Pique could only swipe into his own net despite attempting to clear.
A third was scored with just over ten minutes remaining when Ribery produced a stand-up ball to the back post for Muller to rise above two Barca defenders to powerfully nod home to wrap it all up.
Bayern will now look forward to the May 25 final at Wembley where they will take on German Bundesliga rivals Borussia Dortmund for the chance to atone for last season's penalty shootout loss to Chelsea.
2012/13 UEFA Champions League semi-final - second leg
Nou Camp, Barcelona - 96,636