The Reds scored the opening goal of the tie 26 minutes into the second leg as Sadio Mane controlled Virgil van Dijk's pass, took Manuel Neuer out of the game with a turn just inside the box and clipped the ball into the far corner of the net.
A Joel Matip own goal gave Bayern some hope, but Van Dijk put the visitors back in control of the match and Mane rounded off the scoring late on.
Relive how a famous night for Liverpool unfolded with Sports Mole's live text coverage below.
Bayern have won only one of their eight matches in European competition against the Reds. However, 68% of the 31 previous teams to have drawn 0-0 away from home in the first leg of a Champions League knockout tie have ended up progressing to the next round, so the German champions will consider themselves slight favourites tonight.
STARTING XI: Neuer; Rafinha, Sule, Hummels, Alaba; Thiago, Martinez; Gnabry, Rodriguez, Ribery; Lewandowski
SUBS: Ulreich, Boateng, Goretzka, Davies, Jeong, Coman, Sanches
STARTING XI: Alisson; Alexander-Arnold, Matip, Van Dijk, Robertson; Milner, Wijnaldum, Henderson; Salah, Firmino, Mane
SUBS: Mignolet, Lovren, Fabinho, Lallana, Shaqiri, Origi, Sturridge
6 - No @LFC player has scored more away goals in European Cup/Champions League history than Sadio Mane (6, level with Steven Gerrard and Roberto Firmino). Degree. #BAYLIV pic.twitter.com/oJhQa5WFCo— OptaJoe (@OptaJoe) March 13, 2019
BAYERN MUNICH SUBS: Ulreich, Boateng, Goretzka, Davies, Jeong, Coman, Sanches
LIVERPOOL SUBS: Mignolet, Lovren, Lallana, Shaqiri, Origi, Sturridge