First-half goals from Robert Lewandowski, Jamal Musiala and Leroy Sane put the defending champs on the front foot. Lazio pulled a goal back in the second period but only after a Francesco Acerbi own goal minutes before.
Bayern were off and running after just nine minutes when Lewandowski pounced and scored after a mis-hit back pass from Lazio defender Mateo Musacchio, who was replaced after just 30 minutes.
The goal made Musiala — aged 17 years and 363 days — Bayern’s youngest Champions League goal scorer, the youngest to score for a German club in the competition, and the second-youngest ever to score in a UCL knockout game after Bojan Krkic in 2008.
They were 4-0 up seconds after the restart thanks to Acerbi, who bumbled the ball into his own net after a fine Sane run and cross from the left.
Lazio kept pushing and found some joy seven minutes later after some patient dribbling and a nifty finish from Joaquin Correa at the edge of the box. But it was far too little, much too late for the Serie A side as they now have a mountain to climb in the second leg in Munich on March 17.