The Poland striker, who netted a hat-trick in a 6-0 home demolition of Werder Bremen on the Bundesliga's opening weekend, spurned several chances in either half before he found the back of the net with a trademark clinical finish in the 81st minute.
He then ripped through the home team's defence in stoppage time before squaring a perfect pass for substitute Joshua Kimmich, who sealed the win with an angled shot.
A well-organised Schalke frustrated the visitors for long spells and missed their best chance early in the second half when Dutch striker Klaas Jan Huntelaar rattled the crossbar with a screaming shot from 30 metres.
Despite having several key players injured, Bayern's new coach Carlo Ancelotti was still spoilt for choice from a deep squad and handed Renato Sanches his debut following the midfielder's 35-million euro ($39.8 million) close-season move from Benfica.
Yet the 19-year-old, who helped Portugal win Euro 2016, struggled in his maiden appearance for Bayern as did his team mates against a packed Schalke midfield.
Lewandowski skewed a shot wide in the first half and shot over an empty net from four metres in the second before he finally broke the deadlock.
The 28-year-old hitman took a defence-splitting pass from Javi Martinez in his stride and buried the ball over advancing keeper Ralf Faehrmann from 14 metres.
He missed another close-range sitter in the dying minutes before putting Kimmich through and the versatile midfielder made no mistake from inside the penalty area.
In Saturday's stand-out fixtures, Bayer Leverkusen take on Hamburg and Borussia Dortmund visit promoted RB Leipzig.
(Writing by Zoran Milosavljevic; Editing by Toby Davis)
