Robert Lewandowski converted a penalty before a deft chip from his second-half replacement Eric Maxim Choupo-Moting doubled the advantage on the night. Lazio grabbed a consolation when Marco Parolo was left unmarked to head in a late free-kick from close range.
"The win is very important to us. It's in our DNA that we want to win every game," Bayern midfielder Joshua Kimmich told Sky.
"We played confidently, even if it wasn't a brilliant performance and it was annoying to concede a goal." Their passage into the last eight takes Bayern past Barcelona's tally of 18 Champions League quarter-final appearances since the competition was rebranded from the European Cup.
Lazio coach Simone Inzaghi told Sky. "Some teams are unplayable: Bayern are one of them."