The host's powerful start paid off as Kingsley Coman stunned Luthe with a shot into the top right corner from the edge of the box in the 16th minute.
The visitors responded as Robin Knoche's header forced Bayern goalie Manuel Neuer into action in the 21st minute, before Taiwo Awoniyi's attempt from close range missed the target just wide moments later.
Bayern answered in style and kept relentless in front of the goal. Joshua Kimmich's long ball into the box found Tanguy Nianzou, who headed past Luthe on 25 minutes.
The German giants made it three before the break. Luthe brought down Lewandowski inside the penalty area, and the Pole stepped up to convert the penalty.
Julian Nagelsmann's men came out with their guns blazing after the restart, as Lewandowski wrapped up his brace and his 31st goal of the campaign two minutes into the second half.
Elsewhere, relegation-threatened Hertha Berlin snatched a vital win after upsetting Hoffenheim 3-0 through goals from Niklas Stark, Ishak Belfodil and Lucas Tousart. Mainz cruised 4-0 past bottom side Arminia Bielefeld to end its two-game losing streak. Stuttgart climbed out of the bottom three after bouncing back to beat Augsburg 3-2 while last placed Greuther Furth played out a goalless stalemate with Freiburg.
The match between Bochum and Borussia Monchengladbach on Friday was called off after the linesman got hit by a pint midway through the second half. The referee halted the game with Monchengladbach leading 2-0 on the road.
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