Raheem Sterling had given Chelsea the lead just before half-time, finishing off a brilliant counter-attack by meeting Nicolas Jackson's cross, cutting inside Kyle Walker and curling his shot home.
Already 5-1 ahead after a dominant first-leg showing in the Czech Republic, Darwin Nunez's opener was the first of four goals in seven first-half minutes as the Reds overwhelmed their opponents.
Chris Wood scored a hat-trick on his return to St James' Park as Nottingham Forest ended aseven-game winless run with a stunning Premier League victory at Newcastle.
Jurgen Klopp's continued to push for more goals, but Sven Ulreich was on hand to deny Mohamed Salah and Alberto Morena. Bayern were forced into a change midway through the first half as Thiago Alcantara made way for Renato Sanches.
Injuries to Anthony Martial and Jesse Lingard dented United's attacking thrust and PSG scored twice in seven second-half minutes at Old Trafford on Tuesday to put a foot in the quarter-finals.
Denmark had a nice flurry of attacking action in the final five minutes of the first half, creating a couple of corners and forcing Daniel Emmanuel into one save, but Nigeria was well in control after that.
A dominant first-half display proved enough to give Liverpool victory over Premier League rivals Chelsea, inflicting a first defeat on Antonio Conte and ruining the homecoming of David Luiz.