Jurgen Klopp’s team join Manchester City, Manchester United and Tottenham in Friday’s draw for the last-eight after beating Bayern 3-1 in the second leg of their round of 16 tie at the Allianz Arena.
Last month’s first leg at Anfield had ended goalless.
Thiago Alcantara wasted a good early opportunity for the Bundesliga leaders, who had penalty appeals ignored by the referee when Robert Lewandowski went down under Virgil Van Dijk’s challenge.
The visitors suffered a blow in the 13th minute when Jordan Henderson had to be substituted after picking up a foot injury.
The setback did not put Liverpool off their stride though and, after Robert Firmino had lashed a fierce shot narrowly wide, they took the lead in the 26th minute when Sadio Mane chipped the ball over Bayern goalkeeper Manuel Neuer and into the back of the net.
After Andy Robertson had gone close to doubling Liverpool’s lead, Bayern made it 1-1 six minutes before the interval when Joel Matip deflected Serge Gnabry’s cross into his own net.
The second half ebbed and flowed but Bayern went close to moving ahead when Lewandowski narrowly failed to latch on to another excellent Gnabry cross.
But it was Liverpool that scored the crucial third goal in the 69th minute when the imperious Van Dijk rose highest to head James Milner’s cross past Neuer.
Needing two goals to progress, Bayern never really looked like getting back into the tie and last year’s beaten finalists confirmed their place in this season’s quarter-finals with six minutes left when Mane headed Mo Salah’s cross home.