Pep Guardiola's Bayern side were facing what looked like an impossible task after going down 3-0 in last week's first leg at the Camp Nou, but they were given an early glimmer of hope in the return when the unmarked Medhi Benatia headed home on seven minutes.
However, the final outcome of the tie was put beyond doubt when Luis Suarez twice set up Neymar to score for the visitors before half an hour had been played.
Bayern produced a rousing second-half performance and goals from Robert Lewandowski and Thomas Mueller gave them hope. But Bayern were unable to press their momentum and had to settle for a win on the night.
Barcelona, on the other hand, advanced to the final which will be played in Berlin on June 6.
Luis Enrique's side will face either bitter rivals Real Madrid or Juventus in the final, with the Italians defending a 2-1 first-leg lead in the return at the Santiago Bernabeu on Wednesday.
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