Bayern have now won three games in three without conceding a goal and have one foot in the next round with a five-point lead at the top of Group E.
The six-time European Cup winners were twice denied the lead by VAR in a hard-fought first hour, before Sane finally broke Benfica's defences with a fizzing dead-ball strike 20 minutes from time.
The German international added another goal and an assist in the closing stages as the hosts collapsed and Bayern cruised to yet another comfortable Champions League win this season.
Bayern were without a handful of key names, including Leon Goretzka, Alphonso Davies and head coach Julian Nagelsmann, who was absent with what the club described as a "flu-like infection".
Yet they started brightly with assistant coach Dino Toppmoeller directing proceedings from the sidelines.
October 20, 2021
Robert Lewandowski forced two early saves from Odysseas Vlachodimos, while Leroy Sane shaved the post with a low shot across the face of goal.
Yet the Bundesliga champions' formidable front line became increasingly starved of space as Benfica found their rhythm.
Lewandowski found the net from close range just before half-time, but the goal was ruled out after the replay showed the Polish striker had scored with his arm.
German-born Benfica keeper Vlachodimos pulled off another fine reflex stop to deny Benjamin Pavard just after the break as Bayern once again besieged the Benfica box.
The visitors had another goal ruled out for offside minutes later, before Neuer frustrated Diogo Goncalves with a flying save at the other end.
Roman Yaremchuk also came close for the hosts, before Sane finally secured the lead for Bayern with a dipping free-kick.
Bayern doubled the lead 10 minutes later as Everton directed a Serge Gnabry cross into his own net.
Sane then crowned a perfect evening with an assist and another goal, setting up Lewandowski for Bayern's third before smashing in their fourth himself on the half-volley.
October 20, 2021