Robert Lewandowski opened the scoring with his 72nd goal to overtake Raul as the tournament’s third-highest scorer.
Leroy Sane added a third and then forced an own goal, before Lazio responded through Joaquin Correa.
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Bayern have collected six titles in the past nine months but have dropped points in both their Bundesliga games since winning the Club World Cup.
They were in complete control in the first leg against Lazio, however, after Lewandowski pounced on Mateo Musacchio’s sloppy back pass to round Pepe Reina and slot into an empty net in the ninth minute.
The goal moves him above former Real Madrid and Schalke striker Raul in the Champions League scoring charts, though he is still a long way behind Cristiano Ronaldo (134) and Lionel Messi (119).
Fifteen minutes later, Musiala, an England youth international who is also eligible to play for Germany, slotted a composed finish into the bottom corner to double Bayern’s lead.
In doing so, he surpassed Alex Oxlade-Chamberlain – who netted for Arsenal against Olympiakos in September 2011 at 18 years and 44 days old – as the youngest English scorer in the competition.
Kingsley Coman then toyed with the Lazio defence and when his shot was palmed out by Reina, former Manchester City winger Sane was on hand to tap in a third.
Sane’s dangerous delivery was turned into his own net from close range by Francesco Acerbi immediately after the break to all but wrap up Bayern’s progression to the quarter-finals.
Lazio, on their first appearance in the knockout stages for 21 years, found a consolation when Correa jinked through the Bayern defence for a clever solo goal.
Bayern host Lazio in the return leg on