The visitors started the game on the front foot and went ahead inside the opening nine minutes. An under-hit backpass by Matteo Mussachio was pounced on by Robert Lewandowski, who rounded Pepe Reina before slotting into an empty net.
The game opened up after this, with both sides fashioning good chances. However, it was Bayern Munich who got on the scoresheet once again.
Alphonso Davies showed his trademark skill and speed down the left flank before teeing up Leon Goretzka, who was quickly closed down. The Germany international, in turn, set up Jamal Musiala who scored his first Champions League goal from outside the box.
At 17 years and 363 days, Musiala became the youngest player to ever score a goal for a German club in the Champions League.
Lazio had appealed for a penalty earlier after midfielder Sergej Milinkovic-Savic had been tripped by Jerome Boateng. However, the VAR revealed that he had been offside in the buildup.
Lazio manager Simone Inzaghi made a change soon after, with the hapless Mussachi making way for Senad Lulic. Unfortunately for them, this did little to stem the tide.
Bayern Munich got a third goal in the 42nd minute. Kingsley Coman dispossessed Patric on the midway line and ran over 45 yards, dribbling across Francesco Acerbi before forcing a save from Reina.
Leroy Sane was, however, on hand to score the rebound and give the German champions a three-goal lead at half-time.
The second half started on an even poorer note for Lazio. Acerbi turned into his own net after Sane had ended a devastating counter-attack by squaring the ball into the box in the 47th minute.
Lazio got on the scoresheet two minutes later. Joaquin Correa dribbled across the visitors' defense before beating Manuel Neuer with a low shot.
From then on, it was cruise control for Bayern Munich, although they did manage to force Reina into some smart saves.
The victory gives Bayern Munich an overwhelming advantage to take into the second leg slated for March 17. This also sent a statement of intent to the rest of the continent about their readiness to retain their title.
Here are five talking points from the fixture.
#5 Rampaging Bayern Munich bounce back from weekend's defeat
Bayern Munich have been a bit indifferent in recent weeks and came into this fixture having suffered a 2-1 reversal to Eintracht Frankfurt last weekend.
Lazio, on the other hand, are among the most in-form teams in Serie A. A run of seven wins from their last eight league games had seen them re-establish themselves in the top-four race.
This contrast in form set this fixture up as one to watch but Bayern Munich brought their A-game to the fore to ensure that the hosts did not stand a chance.
The Bavarians' performance was reminiscent of recent Champions League maulings against the likes of Barcelona and Chelsea.
In many ways, a 4-1 defeat flattered Lazio, as Bayern Munich were totally dominant from start to finish.
The victory means that the Bavarians have now gone 17 away games without defeat in the Champions League, which is a tournament record.
This was a perfect response to the weekend's setback, and Hansi Flick will be hoping for more of the same when Bayern take on FC Koln on Saturday.
#4 Joshua Kimmich writes his name in the record books
Joshua Kimmich has grown in leaps and bounds since joining Bayern Munich from RB Leipzig in 2015.
The Germany international initially operated as a right-back but was converted to a central midfielder by Pep Guardiola. He has adapted to the role so well that he was named UEFA's Best Midfielder in 2020.
Kimmich once again starred in the center of the park and gave another stellar display to propel his side to glory.
Despite not getting on the scoresheet or providing an assist, the 26-year-old was still very integral to everything that Flick's side did in Rome. He made a total of five interceptions and had one shot on target, while he also had a staggering pass completion of 93.3%.
Joshua Kimmich made his 50th UEFA Champions League appearance for Bayern Munich, which means that he is now on the record books as the player with the most wins after 50 matches.
The victory was his 38th in the competition, two wins better than the 36 that his teammate Thomas Muller managed.
Kimmich made his Champions League debut in September 2015 when he came off the bench in a 3-0 victory over Olympiacos. Since then, he has gone on to become a mainstay in both the Bayern Munich and German national team set-ups.