The Poland striker scored his first league goal for his new club but a Benedikt Howedes second half goal saw the two sides share the spoils.
Lewandowski opened his Bayern account to put the visiting ahead with a well-worked strike.
Pep Guardiola's side typically dominated the ball, but Sidney Sam's free kick midway through the second half caused chaos in the Bayern box, deflecting off Howedes and into the net.
Replays suggested the ball went in off the Germany defender's arm, but referee Marco Fritz waved away furious Bayern protests.
The result halts Schalke's run of seven consecutive defeats to Bayern, although the team remains without a win this season.
Bayern has lacked a clinical side to its game since switching to Guardiola's now-favored 3-4-3 system, and an inability to break down its opponents will have done little to soothe any nervy fans.
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Bayern, which handed a debut to Xabi Alonso, was made to work for the opening-day win over Wolfsburg last week, but rushed out of the blocks within the opening six minutes in Gelsenkirchen.
Philipp Lahm's ball over the top found Lewandowski, who squared to Thomas Muller, only for the striker's first-time shot to be tipped over the bar by goalkeeper Ralf Fahrmann, who was also forced into producing a smart save to keep out Mario Gotze's low drive.
However, Fahrmann was powerless to prevent the visitors taking a well-deserved lead on the 10-minute mark.
A neat one-two involving Sebastian Rode released Lewandowski inside the penalty area, leaving the Polish striker with a simple finish from close range.
It took 27 minutes for Schalke to muster its first attempt, Sam sending a swerving shot just wide from 30 yards.
Manuel Neuer was nearly caught out five minutes before the break, sending a clearance straight to Kaan Ayhan after rushing out of his area, but the teenage midfielder's audacious 45-yard lob went wide.
Schalke showed more urgency within the opening 10 minutes of the second half.
First Julian Draxler powered a header straight at Neuer, before Eric Maxim Choupo-Moting was denied by Jerome Boateng's last-ditch tackle.
Bayern's defense was finally breached two minutes after the hour mark, when Sam's teasing delivery pinballed around the penalty area before Alonso's clearance cannoned off Howedes and into the net.
Bayern could not channel their frustrations into a winner, with Keller visibly delighted at the final whistle with a result that is likely to dispel any doubts about his job security at Schalke.