The holders were in complete command following a 4-1 first-leg triumph in Rome, and a highly improbable comeback from the Serie A side never looked like coming to pass.
Instead, it was another night that belonged to Bayern talisman Robert Lewandowski, whose 39th goal of the season came via a 33rd-minute penalty.
Eric Maxim Choupo-Moting doubled the lead in the 73rd minute before Marco Parolo belatedly gave Lazio something to celebrate.
While Bayern will need to be more convincing if they are to retain the title, the several other gears they may need to go to in the latter stages were never required here.
Leroy Sane drifted an effort narrowly wide of the right-hand post in the 13th minute in what served as the best chance of the first half until Vedat Muriqi pulled down Leon Goretzka while defending a corner.
Istvan Kovacs pointed to the spot and Lewandowski made no mistake with a stuttered run-up, rattling the ball into the bottom-left corner.
Another defensive lapse from Lazio almost provided a second for Lewandowski, but his near-post effort was repelled by Pepe Reina.
Reina could do nothing as Choupo-Moting lofted a composed finish over him after being played through by David Alaba to add gloss to an already emphatic aggregate scoreline, with Lazio flattered by their consolation when substitute Parolo netted a far-post header from Andreas Pereira's free-kick.
ERIC MAXIM CHOUPO-GALTING! #UCL #FCBLAZ #MiaSanMia pic.twitter.com/06DtUC2GW2— FC Bayern (@FCBayern) March 17, 2021
What does it mean? - Gulf in European pedigree shows in underwhelming spectacle
Bayern are into a competition-record 19th quarter-final, and it would take a brave soul to bet against Hansi Flick's men going all the way for a second successive season.
Lazio should be pleased with reaching the knockout stages in their first Champions League tournament proper appearance since the 2007-08 campaign. Across the two legs, however, this was a tie where the chasm inexperience at this level was telling.
Lucky 13 for Lewy
Lewandowski has scored all 13 penalties he has taken in the Champions League, while no player has more goal involvements in the competition since the start of last season than the Poland international's 25 (20 goals, five assists).
A bad night at both ends for Muriqi
Muriqi demonstrated little aptitude for defending when he hauled down Goretzka to concede the penalty, and the forward did little at the other end either, playing one key pass but not attempting a shot before being taken off in the 56th minute.
Bayern, holding a four-point lead at the top of the Bundesliga, host Stuttgart on Saturday. Lazio are six points adrift of the Champions League places in Serie A and visit Udinese on Sunday.