Having turned down Yevhen Konoplyanka's claims for a spot-kick following a foul by Fernando Muslera early on, referee Benoit Bastien then ruled Breel Embolo had gone down too easily under pressure from Galatasaray's goalkeeper four minutes into the second half.
Muslera had shown his quality with a fine double save from Embolo moments earlier, although his rollercoaster performance looked to have been capped off by a 58th-minute own goal.
But the offside flag came to Galatasaray's rescue to further compound Schalke's frustration as Domenico Tedesco's side had to settle for a point.
Schalke should have been awarded a penalty in the 13th minute, but referee Bastien deemed that Muslera's lunge on Konoplyanka was not a foul, and there was little else in the way of chances until the stroke of half-time.
With Champions League debutant Alexander Nubel having denied Eren Derdiyok from point-blank range, Galatasaray were caught out from the resulting counter, Muslera pulling off an acrobatic save to tip Konoplyanka's strike over.
Muslera was heavily involved after the restart, pulling off two brilliant stops in quick succession to deny Embolo, before the referee again came to the fore.
Embolo had drawn a clumsy tackle from Muslera but, rather than awarding a penalty, Bastien booked the striker for simulation.
Schalke's bad luck seemed to have ended when Embolo's mishit deflected in off Muslera, only for the linesman's flag to cut short their celebrations on a frustrating day for the visitors.
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Although Tedesco will point to Bastien's decisions, Schalke's finishing was wasteful, and they have now squandered a chance to move level on points with Group D leaders Porto.
Galatasaray, meanwhile, must improve if they are to get anything from the return clash in Germany on November 6.
Konoplyanka thrives up top
Konoplyanka has often struggled to nail down a first-team spot at Schalke, but the former Sevilla man put in an impressive display in an unfamiliar central role, with his pace and endeavour proving too much for Galatasaray's defence to handle.
With Schalke having scored just five goals in the Bundesliga so far, Tedesco may have found the solution to their misfiring front line.
Muslera's blushes spared
It was a strange performance from Muslera who, in between committing two fouls that could have resulted in penalties, and conceding an own goal that was subsequently ruled out, the Uruguayan pulled off a string of top-class saves to keep Schalke at bay.
Super Lig leaders Galatasaray face a trip to Yeni Malatyaspor on Sunday, with Schalke travelling to RB Leipzig on the same day.