A solitary goal from Alexander Meier proved the difference, though he should have had another but for a scuffed penalty.
Even with Michael Hector's sending off, it was a much more competent performance from Nico Kovac's side that anything they had put on last season.
Frankfurt firing from the start
The Eagles began with pace and purpose, and a barrage of attempts caught Schalke off guard in the early minutes. Mijat Gacinovic's shot squirmed narrowly wide after Junior Caicara got a crucial touch on the ball. Not long after, Branimir Hrgota collected a lifted through ball from Makoto Hasebe. His shot looked certain to go in, only to hit the bar.
Meier then failed to take advantage of a brilliant Hrgota pass, skying well over the bar. Finally, though, Frankfurt found a way past Ralf Fährmann. Szabolcs Huszti fired the ball into Meier's feet after Schalke passed up possession; two touches later, Meier used his third to slam his shot low into the far bottom corner from the edge of the area.
It could have got even better in the following attack but for Gacinovic's incredible solo goal to be chalked off, correctly, after the ball had gone out of play. Following that, Schalke struggle to work any meaningful opportunities. Klaas-Jan Huntelaar and Eric Maxim Choupo-Moting threatened, however it was no great problem to Lukas Hradecky.
Schalke's late spur not enough to earn a point
Breel Embolo came on at half time but both sides had to rely on set pieces to make any sort of headway in attack. Even then, both goalkeepers were confidently dealing with anything in the air. Embolo's moments of brilliance were few and far between, in what was a dull opening to the half.
It did spark into life when Meier handed chance to score from the spot after Gacinovic was brought down by Caicara. The veteran forward stepped up but his usually trusty right foot failed him on this occasion, as his weak penalty was easily saved by the sprawled Fährmann.
Seemingly, it took Schalke until the 70th minute to realise that they actually need to go forward to score. The Royal Blues turned up the heat after that and were given a great chance to go and get an equaliser when Michael Hector was sent off for hauling down Huntelaar on goal; he collected a quick free-kick, but Hradecky made a great save.
Choupo-Moting fired wide at the death as Frankfurt hung on for a deserved three points, in what was a much improved performance on last season's showings.