Jens Keller's charges went behind early in the Turk Telekom Arena, but fought back with a strike just before half time to leave Didier Drogba and Wesley Sneijder frustrated
Burak Yilmaz had given his side a dream start in the 12th minute with a powerful strike, but the Turkish team were pegged back by Jermaine Jones' leveller and will have to get a result in the second leg to stay in the continental competition.
The Germans were the first team on the offensive, troubling goalkeeper Fernando Muslera after barely a minute had been played. The Uruguayan pulled off a fingertip save from Jermaine Jones, who fired in savagely from out wide after gaining space on the wing. Schalke looked dangerous in the opening minutes, but it would be the Turkish outfit who took the advantage.
Benedikt Howedes looked a safe bet to deal with an intelligent pass lofted through by Selcuk Inan, but the defender and Schalke captain hesitated, failing to take the bouncing ball under control.
Burak Yilmaz took full advantage of Howedes' slip, crashing past his opponent and releasing a powerful effort that gave Timo Hildebrand no chance one-on-one. It was a perfect start for the home side, as they looked to strengthen their case for a spot in the Champions League quarter-final in front of their own fans.
Schalke were unbowed by the early setback, and should have hit back almost immediately through Klaas-Jan Huntelaar. The Netherlands international had crept in unmarked at the far post as Howedes headed a corner powerfully across goal, but somehow he failed to make contact with the ball which flashed past and out of play.
The visitors were pushing hard for an equaliser, and it almost arrived thanks to the unlikely figure of defender Semih Kaya - who came within inches of turning Jefferson Farfan's cross past his own keeper.
The breakthrough for Schalke came in the dying minutes of the first half, the crossbar having already denied Hamit Altintop the chance to double Galatasaray's advantage.
Farfan punched a hole in the home defence with a sparkling run, and was unselfish enough to square to Jones in the box. The midfielder finished impeccably to cap his side's counter, and turn the advantage Schalke's way in the first leg.
Both teams continued to search for victory after the interval, which made for an enthralling clash. Albert Riera forced Hildebrand into action with a cross-shot that was punched clear by the shot-stopper, before Farfan was given an excellent opportunity to give his side a second at the other end.
Julian Draxler surged past the Galatasaray defence and reached the byline, and with the net wide open the Peruvian could only find the legs of Semih with his shot, saving the Turkish side from going behind.
Yilmaz was the next to break through, but was spared the disappointment of failing to beat Hildebrand clean through by a late flag from the linesman. Momentum switched between the two penalty areas, Huntelaar the next to go close with a volley skied over the bar, but in spite of both teams enjoying opportunities there was no breaking the deadlock, and Schalke take a narrow away goal advantage back to Germany.
Schalke and Galatasaray will be back in Champions League action on March 12, when they meet for the last 16 decider in Germany. The Turkish side know they will have to score at least once to avoid elimination.