"It is good for English football,” Liverpool midfielder James Milner told BT Sport. “That's what you want. “
With the sides having drawn 0-0 at Anfield on 19 February, Senegal international Sadio Mané opened the scoring after 26 minutes to give Liverpool a crucial away goal.
Bayern levelled just before half-time when Joel Matip put through his own net.
Needing only parity to advance, Liverpool maintained their composure and then picked off the hosts.
Virgil van Dijk headed in their second from Milner’s corner and with Bayern increasingly witless, Mané bagged his brace six minutes from time.
Lionel Messi also scored twice as Barcelona weathered a Lyon fightback to advance 5-1.
The Argentine struck his first 17 minutes into the second leg from a penalty awarded after Jason Denayer tripped Luis Suarez in the box.
Philippe Coutinho added the second on the half hour to make it 2-0 on aggregate and put the Catalans in control.
However their passage looked far from certain for the 15 minutes following Lucas Tousart’s riposte for the visitors.
But Messi calmed Camp Nou's fraying nerves with his second to make it 3-1 and he then orchestrated the rout setting up Gerard Piqué for the fourth and Ousmane Dembélé for the fifth.
"It was an incredible match for Messi," said Barcelona coach Ernesto Valverde. "He scored and delivered passes for goals. He was there tackling too. Even if we’re used to it, he’s still capable of surprising us.”
Barcelona, who are into the last eight for the 12th consecutive year, are the only Spanish club in the competition following the elimination of Atletico and Real Madrid.
"When Messi is at that kind of level, he is almost unstoppable," said Lyon coach Bruno Genesio. "The final scoreline doesn’t reflect the match. We did what we could."
Liverpool and Barcelona join Porto, Ajax, Juventus, Manchester City, Manchester United and Tottenham Hotspur in the draw on Friday for next month's quarter-final ties.