The Bavarian giants were heavy favourites to progress following a 3-0 first-leg win at Stamford Bridge pre-lockdown, and they got off to the perfect start when Lewandowski stroked home a penalty on 10 minutes.
The Polish hitman then turned provider as he laid on a pass for Ivan Perisic to tuck in the second soon after.
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Chelsea were second best for much of the first half and were left frustrated when Callum Hudson-Odoi's fine finish was ruled out by VAR. However, the visitors did pull one back on the stroke of half time when Tammy Abraham pounced upon an error from Manuel Neuer.
Frank Lampard's men improved after the break, but Bayern remained the greater threat. Substitute Corentin Tolisso made sure of the win before Lewandowski's bullet header sealed a 7-1 success on aggregate.
Bayern will now look ahead to a one-off quarter final showdown with Barcelona in Lisbon on Friday, August 14.
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Brilliant Bayern are just too good. No surprises here. Bayern got the job done with the minimum of fuss. Most of the heavy lifting was done prior to the virus lockdown in a scintillating first-leg showing at Stamford Bridge. The Bundesliga champions will now head to Lisbon for the last eight, where they will undoubtedly be a good bet to lift a sixth European Cup. There's also the small matter of bidding to emulate the treble triumph of 2013. That would take Hansi Flick's first nine months in charge from excellent to exceptional.
As for Chelsea, it's a sad way to end a promising season, but the main thing for Lampard and his young charges is that they will compete in the Champions League again next term. The Blues boss enjoyed a solid first campaign at the helm under some difficult circumstances. Now Chelsea can compete in the transfer market once again, they have already made acquisitions to suggest they will be more of a force both home and abroad - but that defence remains the main cause for concern.
MAN OF THE MATCH
Robert Lewandowski (Bayern). Won and converted the penalty to end any slim hopes of a Chelsea miracle. The Pole then assisted the next two before adding his 13th CL goal of the season as he once again showed why he is one of the finest strikers in the business.
Robert Lewandowski (Bayern Munich)
Image credit: Getty Images
BAYERN MUNICH: Neuer 6, Kimmich 7, Boateng 7, Alaba 7, Davies 8, Goretzka 7, Thiago 8, Muller 7, Gnabry 7, Perisic 7, Lewandowski 9. Subs: Sule 7, Coutinho 6, Tolisso 7, Odriozola 6, Martinez n/a.
CHELSEA: Caballero 6, James 7, Zouma 7, Christensen 6, Emerson 7, Kante 7, Kovacic 6, Barkley 6, Hudson-Odoi 6, Abraham 6, Mount 6. Sub: Giroud n/a.
10' - GOAL! Bayern 1-0 Chelsea (Bayern lead 4-0 on agg). Lewandowski steps up and calmly strokes the ball into the corner from the spot. The kick was awarded after Caballero brought the Pole down. He was initially flagged offside, but a VAR check resulted in the penalty being awarded.
24' - GOAL! Bayern 2-0 Chelsea (Bayern lead 5-0 on agg). Perisic is left in acres on the far right of the area. Lewandowski is able to turn and lay it in to his path for a first-time finish in at the near post.
29' - CHELSEA GOAL RULED OUT! Hudson-Odoi thinks he's reduced the arrears with an exquisite 25-yard effort into the far corner, but VAR chalks it off for offside in the build up.
44' - GOAL! Bayern 2-1 Chelsea (Bayern lead 5-1 on agg). Abraham taps in the rebound after Neuer had spilled Emerson's drilled cross from the left.
76' - GOAL! Bayern 3-1 Chelsea (Bayern lead 6-1 on agg). Tolisso is left free in the six-yard box to volley home Lewandowski's left-wing cross.
83' - GOAL! Bayern 4-1 Chelsea (Bayern lead 7-1 on agg). Lewandowski flies in at the far post to power a superb downward header in to the corner from a right-wing cross.
Chelsea's 7-1 defeat on aggregate to Bayern Munich was the second-heaviest inflicted on an English team in Champions League history, behind only Arsenal's 10-2 aggregate defeat in the last 16 in 2016/17, also against Bayern Munich.
Chelsea conceded 79 goals in all competitions in the 2019/20 season, an average of 1.44 per game - their worst ratio in a season since the 1990/91 campaign (1.64 goals per game conceded).
Lewandowski was involved in all seven of Bayern Munich's goals against Chelsea in the Champions League this season (3 goals, 4 assists). He was the first player to register 3+ goals and assists against an opponent in a season since Luis Figo in 2004/05 vs Roma.
Lewandowski has scored 53 goals in 44 appearances in all competitions this season, finding the net in 36 of those 44 matches.