Jens Keller's side still await victory, while there were wins for Bayer Leverkusen, Mainz and Hertha Berlin along with a six-goal thriller between Hoffenheim and Freiburg
Schalke's disappointing start to the season continued after they suffered a 2-1 defeat to Hannover and were reduced to nine men.
Jens Keller's side have yet to record a victory this season and they got off to the worst possible start on Saturday when defender Benedikt Howedes was dismissed after 15 minutes following a professional foul on Mame Biram Diouf in the penalty area.
Szabolcs Huszti converted the spotkick but would receive his matching orders later on.
The visitors fell further behind when Diouf doubled the advantage shortly before half-time but Adam Szalai did halve the deficit for Schalke 10 minutes after the interval.
Huszti was then sent off 15 minutes from time for serious foul play, before Christian Fuchs was given a second yellow card in the 85th minute as Schalke's nightmare start to the season showed no signs of ending at Hannover.
However, there would be joy for Bayer Leverkusen following a 4-2 home success over Borussia Monchengladbach on Saturday which puts them second.
Stefan Kiessling opened the scoring for the hosts from the spot, before Sidney Sam doubled the advantage.
Martin Stranzl and Juan Arango hit back with two in three minutes for the visitors after the break, but further goals from Sam and Gonzalo Castro sealed the points for the hosts.
Maxim Choupo-Moting and Nicolai Muller gave Mainz a 2-0 victory over Wolfsburg, who had Luiz Gustavo sent off.
Hertha Berlin climbed to sixth as an Adrian Ramos strike proved the difference as they defeated Hamburg 1-0.Hoffenheim and Freiburg draw 3-3 in action packed game at the Rhein-Neckar Arena which also saw three men sent off.
Sejad Salihovic opened the scoring for Hoffenheim in the ninth minute with a penalty before being promptly dismissed for foul and abusive language.
Oliver Sorg equalised four minutes later, before Kevin Volland handed the hosts the lead once more.
Karim Guede equalised on the half-hour mark for Freiburg, who then lost Franics Coquelin before half-time to a second booking.
Sebastian Freis gave the visitors the lead for the first time midway through the second half, but Tobias Strobl equalised with 13 minutes to go and Freiburg's Admir Mehmedi was dismissed at the end of a frantic game.