After finishing with his lowest goal return for four years in 2018-2019, plundering 22 league goals, the Poland international has started the new campaign in electric form and Schalke failed to contain him.
Any hopes Schalke boss David Wagner had of taking points from his first home game in charge were cast into doubt when Lewandowski converted a first-half penalty.
The 31-year-old saved his best for the second half, when he curled a spectacular free-kick into the top corner and then added a third to wrap up a comfortable victory.
Bayern coach Niko Kovac took the opportunity to hand a debut to loanee forward Philippe Coutinho in the last 35 minutes, and after a frustrating start to the season the defending champion is starting to look more like itself.
Schalke goalkeeper Alexander Nubel, heavily linked with a move to Bayern during the close season, made a good reaction save to keep a powerful Lewandowski header out after 15 minutes.
When Schalke's loanee full-back Jonjoe Kenny made a clumsy sliding challenge on Kingsley Coman four minutes later the referee had no option but to award a penalty that Lewandowski calmly stroked into net.
The second half was just four minutes old when Corentin Tolisso won a free-kick 25 yards from goal, prompting Lewandowski to unleash a scintillating strike that swerved away from Nubel and into the top-left corner.
With 15 minutes left, Coman burst down the right and crossed to the edge of the box where Lewandowski had time to take a touch before rattling a low shot into the bottom-right corner of the net to add gloss to the result.